TY  - CONF
AU  - Davidović, Miloš
AU  - Kleut, Duška
AU  - Davidović, Milena D.
AU  - Stojanović, Danka B.
AU  - Jovašević-Stojanović, Milena
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/13046
AB  - Atmospheric aerosols in urban areas typically consist of particles of different diameters, which can range in size from a few nanometers to a few micrometers and can have a strong impact on human health [1,2]. This motivates the need to measure aerosol concentration accurately, but it is often also necessary to combine results from several instruments, with fundamentally different measurement principles. In this work, methods based on the measurement of the electrical mobility of particles, for the range of diameters from 10nm to 420nm, and the measurement of the equivalent optical diameter, for the range of diameters from 300nm to 10um, were used. Combining the overlapping region in two size distribution spectra can be used to infer equivalent optical properties of the ambient aerosol, and examples of measured and combined spectra in several urban hot spots in Bay of Kotor are analyzed in some detail. These examples will illustrate several aspects of urban aerosol properties not readily available in a typical regulatory monitoring setting, such as distribution of modes in number and mass concentration, as well as optical properties of measured aerosol.  As the main result, examples of combining particle size spectrums are presented. In the process of combining the particle size spectra, it is possible to modify the distribution obtained by optical measurements by searching for the optimal value of the refractive index of the particles to obtain the best possible agreement with the size distribution obtained by measuring the electrical mobility. An equivalent refractive index as well as the equivalent shape factor of the ambient aerosol is obtained using Mie scattering theory as a theoretical framework [3]. The measurement results from the mobile monitoring campaign in Bay of Kotor in 2017 were used to elucidate the main principles of size spectrum combination, as well as to showcase diversity of equivalent optical properties of urban aerosols.
PB  - Belgrade : Institute of Physics
C3  - 16th Photonics Workshop : Book of abstracts
T1  - Combining size distribution spectrums of ambient aerosols using equivalent optical properties of nanosized particles – selected examples from the Bay of Kotor
SP  - 26
EP  - 26
UR  - https://hdl.handle.net/21.15107/rcub_vinar_13046
ER  - 

@conference{
author = "Davidović, Miloš and Kleut, Duška and Davidović, Milena D. and Stojanović, Danka B. and Jovašević-Stojanović, Milena",
year = "2023",
abstract = "Atmospheric aerosols in urban areas typically consist of particles of different diameters, which can range in size from a few nanometers to a few micrometers and can have a strong impact on human health [1,2]. This motivates the need to measure aerosol concentration accurately, but it is often also necessary to combine results from several instruments, with fundamentally different measurement principles. In this work, methods based on the measurement of the electrical mobility of particles, for the range of diameters from 10nm to 420nm, and the measurement of the equivalent optical diameter, for the range of diameters from 300nm to 10um, were used. Combining the overlapping region in two size distribution spectra can be used to infer equivalent optical properties of the ambient aerosol, and examples of measured and combined spectra in several urban hot spots in Bay of Kotor are analyzed in some detail. These examples will illustrate several aspects of urban aerosol properties not readily available in a typical regulatory monitoring setting, such as distribution of modes in number and mass concentration, as well as optical properties of measured aerosol.  As the main result, examples of combining particle size spectrums are presented. In the process of combining the particle size spectra, it is possible to modify the distribution obtained by optical measurements by searching for the optimal value of the refractive index of the particles to obtain the best possible agreement with the size distribution obtained by measuring the electrical mobility. An equivalent refractive index as well as the equivalent shape factor of the ambient aerosol is obtained using Mie scattering theory as a theoretical framework [3]. The measurement results from the mobile monitoring campaign in Bay of Kotor in 2017 were used to elucidate the main principles of size spectrum combination, as well as to showcase diversity of equivalent optical properties of urban aerosols.",
publisher = "Belgrade : Institute of Physics",
journal = "16th Photonics Workshop : Book of abstracts",
title = "Combining size distribution spectrums of ambient aerosols using equivalent optical properties of nanosized particles – selected examples from the Bay of Kotor",
pages = "26-26",
url = "https://hdl.handle.net/21.15107/rcub_vinar_13046"
}

Davidović, M., Kleut, D., Davidović, M. D., Stojanović, D. B.,& Jovašević-Stojanović, M.. (2023). Combining size distribution spectrums of ambient aerosols using equivalent optical properties of nanosized particles – selected examples from the Bay of Kotor. in 16th Photonics Workshop : Book of abstracts
Belgrade : Institute of Physics., 26-26.
https://hdl.handle.net/21.15107/rcub_vinar_13046

Davidović M, Kleut D, Davidović MD, Stojanović DB, Jovašević-Stojanović M. Combining size distribution spectrums of ambient aerosols using equivalent optical properties of nanosized particles – selected examples from the Bay of Kotor. in 16th Photonics Workshop : Book of abstracts. 2023;:26-26.
https://hdl.handle.net/21.15107/rcub_vinar_13046 .

Davidović, Miloš, Kleut, Duška, Davidović, Milena D., Stojanović, Danka B., Jovašević-Stojanović, Milena, "Combining size distribution spectrums of ambient aerosols using equivalent optical properties of nanosized particles – selected examples from the Bay of Kotor" in 16th Photonics Workshop : Book of abstracts (2023):26-26,
https://hdl.handle.net/21.15107/rcub_vinar_13046 .

TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Milena D.
AU  - Davidović, Ljubica D.
AU  - Davidović, Miloš D.
AU  - Davidović, Dragomir M.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9164
AB  - We consider the system of N two-level atoms, of which N0 atoms are unexcited and N1 are excited. This system of N two-level atoms, which forms a linear quantum amplifier, interacts with a single-mode electromagnetic field. The problem of amplification of the L-photon states using such an amplifier is studied. The evolution of the electromagnetic field density matrix is described by the master equation for the field under amplification. The dynamics of this process is such that it can be described as the transformation of the scale of the phase space. The exact solution of the master equation is expressed using the transformed Husimi function of the L-quantum state of the harmonic oscillator. The properties of this function are studied and using it the average photon number and its fluctuations in the amplified state are found. © 2021, Editura Academiei Romane. All rights reserved.
T2  - Romanian Reports in Physics
T1  - Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier
VL  - 73
IS  - 1
SP  - 102
UR  - https://hdl.handle.net/21.15107/rcub_vinar_9164
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Milena D. and Davidović, Ljubica D. and Davidović, Miloš D. and Davidović, Dragomir M.",
year = "2021",
abstract = "We consider the system of N two-level atoms, of which N0 atoms are unexcited and N1 are excited. This system of N two-level atoms, which forms a linear quantum amplifier, interacts with a single-mode electromagnetic field. The problem of amplification of the L-photon states using such an amplifier is studied. The evolution of the electromagnetic field density matrix is described by the master equation for the field under amplification. The dynamics of this process is such that it can be described as the transformation of the scale of the phase space. The exact solution of the master equation is expressed using the transformed Husimi function of the L-quantum state of the harmonic oscillator. The properties of this function are studied and using it the average photon number and its fluctuations in the amplified state are found. © 2021, Editura Academiei Romane. All rights reserved.",
journal = "Romanian Reports in Physics",
title = "Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier",
volume = "73",
number = "1",
pages = "102",
url = "https://hdl.handle.net/21.15107/rcub_vinar_9164"
}

Andreev, V. A., Davidović, M. D., Davidović, L. D., Davidović, M. D.,& Davidović, D. M.. (2021). Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier. in Romanian Reports in Physics, 73(1), 102.
https://hdl.handle.net/21.15107/rcub_vinar_9164

Andreev VA, Davidović MD, Davidović LD, Davidović MD, Davidović DM. Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier. in Romanian Reports in Physics. 2021;73(1):102.
https://hdl.handle.net/21.15107/rcub_vinar_9164 .

Andreev, Vladimir A., Davidović, Milena D., Davidović, Ljubica D., Davidović, Miloš D., Davidović, Dragomir M., "Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier" in Romanian Reports in Physics, 73, no. 1 (2021):102,
https://hdl.handle.net/21.15107/rcub_vinar_9164 .

TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Milena D.
AU  - Davidović, Ljubica D.
AU  - Davidović, Miloš D.
AU  - Davidović, Dragomir M.
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8628
AB  - We consider a linear quantum amplifier consisting of NA two-level atoms and study the problem of amplification of N-photon states. The N-photon states are associated with N-quantum states of the harmonic oscillator. We show that the process of interaction of the electromagnetic field with atoms can be associated with some transformation of the phase space and functions defined on this phase space. We consider the Husimi functions QN(q, p) of N-quantum states of the harmonic oscillator, which are defined on the phase space, investigate transformation of these functions, and find an explicit form of the density matrix of the amplified N-photon state. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
T2  - Journal of Russian Laser Research
T1  - Linear Light Amplifier and Amplification of N-Photon States
VL  - 40
IS  - 4
SP  - 321
EP  - 327
DO  - 10.1007/s10946-019-09807-2
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Milena D. and Davidović, Ljubica D. and Davidović, Miloš D. and Davidović, Dragomir M.",
year = "2019",
abstract = "We consider a linear quantum amplifier consisting of NA two-level atoms and study the problem of amplification of N-photon states. The N-photon states are associated with N-quantum states of the harmonic oscillator. We show that the process of interaction of the electromagnetic field with atoms can be associated with some transformation of the phase space and functions defined on this phase space. We consider the Husimi functions QN(q, p) of N-quantum states of the harmonic oscillator, which are defined on the phase space, investigate transformation of these functions, and find an explicit form of the density matrix of the amplified N-photon state. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.",
journal = "Journal of Russian Laser Research",
title = "Linear Light Amplifier and Amplification of N-Photon States",
volume = "40",
number = "4",
pages = "321-327",
doi = "10.1007/s10946-019-09807-2"
}

Andreev, V. A., Davidović, M. D., Davidović, L. D., Davidović, M. D.,& Davidović, D. M.. (2019). Linear Light Amplifier and Amplification of N-Photon States. in Journal of Russian Laser Research, 40(4), 321-327.
https://doi.org/10.1007/s10946-019-09807-2

Andreev VA, Davidović MD, Davidović LD, Davidović MD, Davidović DM. Linear Light Amplifier and Amplification of N-Photon States. in Journal of Russian Laser Research. 2019;40(4):321-327.
doi:10.1007/s10946-019-09807-2 .

Andreev, Vladimir A., Davidović, Milena D., Davidović, Ljubica D., Davidović, Miloš D., Davidović, Dragomir M., "Linear Light Amplifier and Amplification of N-Photon States" in Journal of Russian Laser Research, 40, no. 4 (2019):321-327,
https://doi.org/10.1007/s10946-019-09807-2 . .

TY  - JOUR
AU  - Davidović, Milena D.
AU  - Davidović, Miloš D.
AU  - Sanz, Angel S.
AU  - Božić, Mirjana
AU  - Vasiljević, Darko
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7965
AB  - In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where the diffraction of laser light appears in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. On both sides of the edge, there are also very long light traces along the normal to the edge of the obstacle. The theoretical explanation of this phenomenon is based on the Fresnel–Kirchhoff diffraction theory applied to the Gaussian beam propagation behind the obstacle. In this paper, we supplement this explanation by considering electromagnetic flow lines, which provide a more complete interpretation of the phenomenon in terms of electric and magnetic fields and flux lines; at the same time, that can be related to average photon paths. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
T2  - Journal of Russian Laser Research
T1  - Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge
VL  - 39
IS  - 5
SP  - 438
EP  - 447
DO  - 10.1007/s10946-018-9738-9
ER  - 

@article{
author = "Davidović, Milena D. and Davidović, Miloš D. and Sanz, Angel S. and Božić, Mirjana and Vasiljević, Darko",
year = "2018",
abstract = "In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where the diffraction of laser light appears in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. On both sides of the edge, there are also very long light traces along the normal to the edge of the obstacle. The theoretical explanation of this phenomenon is based on the Fresnel–Kirchhoff diffraction theory applied to the Gaussian beam propagation behind the obstacle. In this paper, we supplement this explanation by considering electromagnetic flow lines, which provide a more complete interpretation of the phenomenon in terms of electric and magnetic fields and flux lines; at the same time, that can be related to average photon paths. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.",
journal = "Journal of Russian Laser Research",
title = "Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge",
volume = "39",
number = "5",
pages = "438-447",
doi = "10.1007/s10946-018-9738-9"
}

Davidović, M. D., Davidović, M. D., Sanz, A. S., Božić, M.,& Vasiljević, D.. (2018). Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge. in Journal of Russian Laser Research, 39(5), 438-447.
https://doi.org/10.1007/s10946-018-9738-9

Davidović MD, Davidović MD, Sanz AS, Božić M, Vasiljević D. Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge. in Journal of Russian Laser Research. 2018;39(5):438-447.
doi:10.1007/s10946-018-9738-9 .

Davidović, Milena D., Davidović, Miloš D., Sanz, Angel S., Božić, Mirjana, Vasiljević, Darko, "Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge" in Journal of Russian Laser Research, 39, no. 5 (2018):438-447,
https://doi.org/10.1007/s10946-018-9738-9 . .

TY  - CONF
AU  - Davidović, Milena D.
AU  - Davidović, Miloš D.
AU  - Davidović, Ljubica D.
AU  - Andreev, Vladimir A.
AU  - Davidović, Dragomir M.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10941
AB  - Many real-world signals, occurring in everyday engineering practice are non-stationary, and as a result, their frequency components may change gradually or abruptly over time. Such signals are typically analyzed using Fourier transform, however, this type of analysis is often not sufficient to reveal the true nature of localized (in time) frequency content. This is where time-frequency analysis (TFA) can be of great help. Several approaches of TFA exist, and in this paper we use Husimi function (Gaussian smoothed Wigner function) for this purpose [1,2,3]. Both the Wigner and Husimi functions are the phase space quasidistributions in quantum mechanics [4,5]. In quantum mechanics, Husimi function of a quantum mechanical state arises when simultaneous measurement of quantum conjugated observables - coordinate and momentum, is performed. Similarly, in signal analysis, conjugated variables are time and frequency. If the measurement has the highest physically possible accuracy (as dictated by the Heisenberg uncertainty relations), then the product of standard deviations of conjugated observables equals  2 and Gaussian smoothed Wigner function for in such a way chosen parameters is known as a Husimi function (HF) [2,5]. In this paper, characteristic signals which describe behavior of several devices used in optics, microwave engineering and plasmonics were obtained via 3D electromagnetic numerical simulations. These signals, and their time and frequency evolution, were then analyzed using specifically tailored HF.
PB  - Belgrade : Institute of Physics Belgrade
C3  - PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts
T1  - Husimi function for time-frequency analysis in optical, microwave and plasmonics aplications
SP  - 59
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10941
ER  - 

@conference{
author = "Davidović, Milena D. and Davidović, Miloš D. and Davidović, Ljubica D. and Andreev, Vladimir A. and Davidović, Dragomir M.",
year = "2017",
abstract = "Many real-world signals, occurring in everyday engineering practice are non-stationary, and as a result, their frequency components may change gradually or abruptly over time. Such signals are typically analyzed using Fourier transform, however, this type of analysis is often not sufficient to reveal the true nature of localized (in time) frequency content. This is where time-frequency analysis (TFA) can be of great help. Several approaches of TFA exist, and in this paper we use Husimi function (Gaussian smoothed Wigner function) for this purpose [1,2,3]. Both the Wigner and Husimi functions are the phase space quasidistributions in quantum mechanics [4,5]. In quantum mechanics, Husimi function of a quantum mechanical state arises when simultaneous measurement of quantum conjugated observables - coordinate and momentum, is performed. Similarly, in signal analysis, conjugated variables are time and frequency. If the measurement has the highest physically possible accuracy (as dictated by the Heisenberg uncertainty relations), then the product of standard deviations of conjugated observables equals  2 and Gaussian smoothed Wigner function for in such a way chosen parameters is known as a Husimi function (HF) [2,5]. In this paper, characteristic signals which describe behavior of several devices used in optics, microwave engineering and plasmonics were obtained via 3D electromagnetic numerical simulations. These signals, and their time and frequency evolution, were then analyzed using specifically tailored HF.",
publisher = "Belgrade : Institute of Physics Belgrade",
journal = "PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts",
title = "Husimi function for time-frequency analysis in optical, microwave and plasmonics aplications",
pages = "59",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10941"
}

Davidović, M. D., Davidović, M. D., Davidović, L. D., Andreev, V. A.,& Davidović, D. M.. (2017). Husimi function for time-frequency analysis in optical, microwave and plasmonics aplications. in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts
Belgrade : Institute of Physics Belgrade., 59.
https://hdl.handle.net/21.15107/rcub_vinar_10941

Davidović MD, Davidović MD, Davidović LD, Andreev VA, Davidović DM. Husimi function for time-frequency analysis in optical, microwave and plasmonics aplications. in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts. 2017;:59.
https://hdl.handle.net/21.15107/rcub_vinar_10941 .

Davidović, Milena D., Davidović, Miloš D., Davidović, Ljubica D., Andreev, Vladimir A., Davidović, Dragomir M., "Husimi function for time-frequency analysis in optical, microwave and plasmonics aplications" in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts (2017):59,
https://hdl.handle.net/21.15107/rcub_vinar_10941 .

TY  - CONF
AU  - Davidović, Milena D.
AU  - Davidović, Miloš D.
AU  - Sanz, Angel S.
AU  - Božić, Mirjana
AU  - Vasiljević, Darko
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10950
AB  - Bohmian mechanics enables visualization and interpretation of quantum mechanical behavior of massive particles through trajectories connected to the probability current density [1]. Electromagnetic field also admits hydrodynamic formulation when the existence of suitably defined photon wave function is assumed [2]. This formulation gives possibility to interpret the optical phenomena in a picturesque way through photon trajectories which describe the evolution of the electromagnetic energy density behind an obstacle. This approach, based on the trajectories, was used in the analysis of modified Young’s double slit diffraction [3], in the context of the Arago-Fresnel laws [4], as well as in the analysis of the modes in the optical and microwave waveguides [5]. A group of scientists from the University of Toronto under the guidance of professor Steinberg, has been able to experimentally determine the mean paths of single photons in the Young’s experiment [6]. The measured trajectories show good agreement with theoretically anticipated trajectories presented in [2, 3]. The achievement of Steinberg’s group was selected by the Physics World as the top breakthrough in physics for the year 2011, as the discovery that is ‘shifting the moral of quantum measurement’ [7]. Theoretical solution for the diffraction of plane wave by the edge of the perfectly conducting plane was given by Sommerfeld in 1896 [8], and this solution became the starting point in solving the diffraction problems for various two dimensional obstacles [9, 10]. Diffraction of Gaussian beam by the edge was studied since the sixties of the last century [11] but more attention was given to the central part of the diffraction image, while the less pronounced side trails were analyzed much later [12]. In this paper we use photon trajectories approach to analyze the diffraction pattern obtained on the screen put behind the laser beam partially covered by a sharp edge, such as a razor blade.
PB  - Belgrade : Institute of Physics Belgrade
C3  - PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts
T1  - Trajectory based interpretation of the laser light diffraction on a sharp edge
SP  - 220
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10950
ER  - 

@conference{
author = "Davidović, Milena D. and Davidović, Miloš D. and Sanz, Angel S. and Božić, Mirjana and Vasiljević, Darko",
year = "2017",
abstract = "Bohmian mechanics enables visualization and interpretation of quantum mechanical behavior of massive particles through trajectories connected to the probability current density [1]. Electromagnetic field also admits hydrodynamic formulation when the existence of suitably defined photon wave function is assumed [2]. This formulation gives possibility to interpret the optical phenomena in a picturesque way through photon trajectories which describe the evolution of the electromagnetic energy density behind an obstacle. This approach, based on the trajectories, was used in the analysis of modified Young’s double slit diffraction [3], in the context of the Arago-Fresnel laws [4], as well as in the analysis of the modes in the optical and microwave waveguides [5]. A group of scientists from the University of Toronto under the guidance of professor Steinberg, has been able to experimentally determine the mean paths of single photons in the Young’s experiment [6]. The measured trajectories show good agreement with theoretically anticipated trajectories presented in [2, 3]. The achievement of Steinberg’s group was selected by the Physics World as the top breakthrough in physics for the year 2011, as the discovery that is ‘shifting the moral of quantum measurement’ [7]. Theoretical solution for the diffraction of plane wave by the edge of the perfectly conducting plane was given by Sommerfeld in 1896 [8], and this solution became the starting point in solving the diffraction problems for various two dimensional obstacles [9, 10]. Diffraction of Gaussian beam by the edge was studied since the sixties of the last century [11] but more attention was given to the central part of the diffraction image, while the less pronounced side trails were analyzed much later [12]. In this paper we use photon trajectories approach to analyze the diffraction pattern obtained on the screen put behind the laser beam partially covered by a sharp edge, such as a razor blade.",
publisher = "Belgrade : Institute of Physics Belgrade",
journal = "PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts",
title = "Trajectory based interpretation of the laser light diffraction on a sharp edge",
pages = "220",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10950"
}

Davidović, M. D., Davidović, M. D., Sanz, A. S., Božić, M.,& Vasiljević, D.. (2017). Trajectory based interpretation of the laser light diffraction on a sharp edge. in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts
Belgrade : Institute of Physics Belgrade., 220.
https://hdl.handle.net/21.15107/rcub_vinar_10950

Davidović MD, Davidović MD, Sanz AS, Božić M, Vasiljević D. Trajectory based interpretation of the laser light diffraction on a sharp edge. in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts. 2017;:220.
https://hdl.handle.net/21.15107/rcub_vinar_10950 .

Davidović, Milena D., Davidović, Miloš D., Sanz, Angel S., Božić, Mirjana, Vasiljević, Darko, "Trajectory based interpretation of the laser light diffraction on a sharp edge" in PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts (2017):220,
https://hdl.handle.net/21.15107/rcub_vinar_10950 .

TY  - JOUR
AU  - Andreev, V. A.
AU  - Davidović, Dragomir M.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena D.
AU  - Davidović, Miloš D.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1685
AB  - We consider scale transformations (q, p) - GT (lambda q, lambda p) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson-Schrodinger uncertainty relations for stretched states.
T2  - Theoretical and Mathematical Physics
T1  - Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator
VL  - 192
IS  - 1
SP  - 1080
EP  - 1096
DO  - 10.1134/S0040577917070091
ER  - 

@article{
author = "Andreev, V. A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena D. and Davidović, Miloš D.",
year = "2017",
abstract = "We consider scale transformations (q, p) - GT (lambda q, lambda p) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson-Schrodinger uncertainty relations for stretched states.",
journal = "Theoretical and Mathematical Physics",
title = "Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator",
volume = "192",
number = "1",
pages = "1080-1096",
doi = "10.1134/S0040577917070091"
}

Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M. D.,& Davidović, M. D.. (2017). Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator. in Theoretical and Mathematical Physics, 192(1), 1080-1096.
https://doi.org/10.1134/S0040577917070091

Andreev VA, Davidović DM, Davidović LD, Davidović MD, Davidović MD. Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator. in Theoretical and Mathematical Physics. 2017;192(1):1080-1096.
doi:10.1134/S0040577917070091 .

Andreev, V. A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milena D., Davidović, Miloš D., "Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator" in Theoretical and Mathematical Physics, 192, no. 1 (2017):1080-1096,
https://doi.org/10.1134/S0040577917070091 . .

TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Dragomir M.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena D.
AU  - Davidović, Miloš D.
AU  - Zotov, Sergey D.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1310
AB  - We consider the Husimi Q(q, p)-functions which are quantum quasiprobability distributions on the phase space. It is known that, under a scaling transform (q; p) - GT (aiiq; aiip), the Husimi function of any physical state is converted into a function which is also the Husimi function of some physical state. More precisely, it has been proved that, if Q(q, p) is the Husimi function, the function aii(2) Q(aiiq; aiip) is also the Husimi function. We call a state with the Husimi function aii(2) Q(aiiq; aiip) the stretched state and investigate the properties of the stretched Fock states. These states can be obtained as a result of applying the scaling transform to the Fock states of the harmonic oscillator. The harmonic-oscillator Fock states are pure states, but the stretched Fock states are mixed states. We find the density matrices of stretched Fock states in an explicit form. Their structure can be described with the help of negative binomial distributions. We present the graphs of distributions of negative binomial coefficients for different stretched Fock states and show the von Neumann entropy of the simplest stretched Fock state.
T2  - Journal of Russian Laser Research
T1  - Scaling Transform and Stretched States in Quantum Mechanics
VL  - 37
IS  - 5
SP  - 434
EP  - 439
DO  - 10.1007/s10946-016-9594-4
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena D. and Davidović, Miloš D. and Zotov, Sergey D.",
year = "2016",
abstract = "We consider the Husimi Q(q, p)-functions which are quantum quasiprobability distributions on the phase space. It is known that, under a scaling transform (q; p) - GT (aiiq; aiip), the Husimi function of any physical state is converted into a function which is also the Husimi function of some physical state. More precisely, it has been proved that, if Q(q, p) is the Husimi function, the function aii(2) Q(aiiq; aiip) is also the Husimi function. We call a state with the Husimi function aii(2) Q(aiiq; aiip) the stretched state and investigate the properties of the stretched Fock states. These states can be obtained as a result of applying the scaling transform to the Fock states of the harmonic oscillator. The harmonic-oscillator Fock states are pure states, but the stretched Fock states are mixed states. We find the density matrices of stretched Fock states in an explicit form. Their structure can be described with the help of negative binomial distributions. We present the graphs of distributions of negative binomial coefficients for different stretched Fock states and show the von Neumann entropy of the simplest stretched Fock state.",
journal = "Journal of Russian Laser Research",
title = "Scaling Transform and Stretched States in Quantum Mechanics",
volume = "37",
number = "5",
pages = "434-439",
doi = "10.1007/s10946-016-9594-4"
}

Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M. D., Davidović, M. D.,& Zotov, S. D.. (2016). Scaling Transform and Stretched States in Quantum Mechanics. in Journal of Russian Laser Research, 37(5), 434-439.
https://doi.org/10.1007/s10946-016-9594-4

Andreev VA, Davidović DM, Davidović LD, Davidović MD, Davidović MD, Zotov SD. Scaling Transform and Stretched States in Quantum Mechanics. in Journal of Russian Laser Research. 2016;37(5):434-439.
doi:10.1007/s10946-016-9594-4 .

Andreev, Vladimir A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milena D., Davidović, Miloš D., Zotov, Sergey D., "Scaling Transform and Stretched States in Quantum Mechanics" in Journal of Russian Laser Research, 37, no. 5 (2016):434-439,
https://doi.org/10.1007/s10946-016-9594-4 . .

TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Milena D.
AU  - Davidovic, Ljubica D.
AU  - Davidović, Miloš D.
AU  - Davidović, Dragomir M.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/643
AB  - We propose a new method for the derivation of Husimi symbols, for operators that are given in the form of products of an arbitrary number of coordinates, and momentum operators, in an arbitrary order. For such an operator, in the standard approach, one expresses coordinate and momentum operators as a linear combination of the creation and annihilation operators, and then uses the antinormal ordering to obtain the final form of the symbol. In our method, one obtains the Husimi symbol in a much more straightforward fashion, departing directly from operator explicit form without transforming it through creation and annihilation operators. With this method the mean values of some operators are found. It is shown how the Heisenberg and the Schrodinger-Robertson uncertainty relations, for position and momentum, are transformed under scale transformation (q; p) - GT (lambda q; lambda p). The physical sense of some states which can be constructed with this transformation is also discussed.
T2  - Physica Scripta
T1  - Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations
VL  - 90
IS  - 7
DO  - 10.1088/0031-8949/90/7/074023
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Milena D. and Davidovic, Ljubica D. and Davidović, Miloš D. and Davidović, Dragomir M.",
year = "2015",
abstract = "We propose a new method for the derivation of Husimi symbols, for operators that are given in the form of products of an arbitrary number of coordinates, and momentum operators, in an arbitrary order. For such an operator, in the standard approach, one expresses coordinate and momentum operators as a linear combination of the creation and annihilation operators, and then uses the antinormal ordering to obtain the final form of the symbol. In our method, one obtains the Husimi symbol in a much more straightforward fashion, departing directly from operator explicit form without transforming it through creation and annihilation operators. With this method the mean values of some operators are found. It is shown how the Heisenberg and the Schrodinger-Robertson uncertainty relations, for position and momentum, are transformed under scale transformation (q; p) - GT (lambda q; lambda p). The physical sense of some states which can be constructed with this transformation is also discussed.",
journal = "Physica Scripta",
title = "Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations",
volume = "90",
number = "7",
doi = "10.1088/0031-8949/90/7/074023"
}

Andreev, V. A., Davidović, M. D., Davidovic, L. D., Davidović, M. D.,& Davidović, D. M.. (2015). Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations. in Physica Scripta, 90(7).
https://doi.org/10.1088/0031-8949/90/7/074023

Andreev VA, Davidović MD, Davidovic LD, Davidović MD, Davidović DM. Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations. in Physica Scripta. 2015;90(7).
doi:10.1088/0031-8949/90/7/074023 .

Andreev, Vladimir A., Davidović, Milena D., Davidovic, Ljubica D., Davidović, Miloš D., Davidović, Dragomir M., "Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations" in Physica Scripta, 90, no. 7 (2015),
https://doi.org/10.1088/0031-8949/90/7/074023 . .

TY  - JOUR
AU  - Andreev, V. A.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena D.
AU  - Davidović, Miloš D.
AU  - Manko, V. I.
AU  - Manko, M. A.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6033
AB  - We propose a new method for calculating Husimi symbols of operators. In contrast to the standard method, it does not require using the anti-normal-ordering procedure. According to this method, the coordinate and momentum operators (q) over cap and (p) over cap are assigned other operators (X) over cap and (P) over cap satisfying the same commutation relations. We then find the result of acting with the (X) over cap and (P) over cap operators and also polynomials in these operators on the Husimi function. After the obtained expression is integrated over the phase space coordinates, the integrand becomes a Husimi function times the symbol of the operator chosen to act on that function. We explicitly evaluate the Husimi symbols for operators that are powers of (X) over cap or (P) over cap.
T2  - Theoretical and Mathematical Physics
T1  - Operator Method for Calculating Q Symbols and Their Relation to Weyl-Wigner Symbols and Symplectic Tomogram Symbols
VL  - 179
IS  - 2
SP  - 559
EP  - 573
DO  - 10.1007/s11232-014-0162-1
ER  - 

@article{
author = "Andreev, V. A. and Davidović, Ljubica D. and Davidović, Milena D. and Davidović, Miloš D. and Manko, V. I. and Manko, M. A.",
year = "2014",
abstract = "We propose a new method for calculating Husimi symbols of operators. In contrast to the standard method, it does not require using the anti-normal-ordering procedure. According to this method, the coordinate and momentum operators (q) over cap and (p) over cap are assigned other operators (X) over cap and (P) over cap satisfying the same commutation relations. We then find the result of acting with the (X) over cap and (P) over cap operators and also polynomials in these operators on the Husimi function. After the obtained expression is integrated over the phase space coordinates, the integrand becomes a Husimi function times the symbol of the operator chosen to act on that function. We explicitly evaluate the Husimi symbols for operators that are powers of (X) over cap or (P) over cap.",
journal = "Theoretical and Mathematical Physics",
title = "Operator Method for Calculating Q Symbols and Their Relation to Weyl-Wigner Symbols and Symplectic Tomogram Symbols",
volume = "179",
number = "2",
pages = "559-573",
doi = "10.1007/s11232-014-0162-1"
}

Andreev, V. A., Davidović, L. D., Davidović, M. D., Davidović, M. D., Manko, V. I.,& Manko, M. A.. (2014). Operator Method for Calculating Q Symbols and Their Relation to Weyl-Wigner Symbols and Symplectic Tomogram Symbols. in Theoretical and Mathematical Physics, 179(2), 559-573.
https://doi.org/10.1007/s11232-014-0162-1

Andreev VA, Davidović LD, Davidović MD, Davidović MD, Manko VI, Manko MA. Operator Method for Calculating Q Symbols and Their Relation to Weyl-Wigner Symbols and Symplectic Tomogram Symbols. in Theoretical and Mathematical Physics. 2014;179(2):559-573.
doi:10.1007/s11232-014-0162-1 .

Andreev, V. A., Davidović, Ljubica D., Davidović, Milena D., Davidović, Miloš D., Manko, V. I., Manko, M. A., "Operator Method for Calculating Q Symbols and Their Relation to Weyl-Wigner Symbols and Symplectic Tomogram Symbols" in Theoretical and Mathematical Physics, 179, no. 2 (2014):559-573,
https://doi.org/10.1007/s11232-014-0162-1 . .

TY  - JOUR
AU  - Davidović, Miloš D.
AU  - Davidović, Milena D.
AU  - Srećković, Milesa
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10951
AB  - Husimi function originated in phase space formulation of quantum mechanics. This function appears naturally whenever simultaneous measurement of coordinate and impulse with maximal accuracy allowed by the Heisenberg uncertainty relation is performed on a given quantum state and it represents the probability distribution for simultaneous unsharp measurement of coordinate and impulse. Husimi function may analogously be defined for any pair of conjugated variables. In analysis of time varying signals these variables are time and frequency. In this paper we consider Husimi function in time-frequency space, we derive some properties of the function and give time-frequency analysis of some characteristic signals.
AB  - U ovom radu razmotrena je Husimijeva funkcija na prostoru kanonski spregnutih promenljivih vreme-frekvencija. Izvedene su neke njene nove osobine koje su ilustrovane na nekoliko analitički zadatih signala. Pokazano je da se Husimijeva funkcija može koristiti pri vremensko-frekvencijskoj analizi signala.
T2  - Tehnika
T1  - Use of Husimi function in time frequency signal analysis
T1  - Primena Husimijeve funkcije u vremensko-frekvencijskoj analizi signala
VL  - 68
IS  - 5
SP  - 905
EP  - 909
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10951
ER  - 

@article{
author = "Davidović, Miloš D. and Davidović, Milena D. and Srećković, Milesa",
year = "2013",
abstract = "Husimi function originated in phase space formulation of quantum mechanics. This function appears naturally whenever simultaneous measurement of coordinate and impulse with maximal accuracy allowed by the Heisenberg uncertainty relation is performed on a given quantum state and it represents the probability distribution for simultaneous unsharp measurement of coordinate and impulse. Husimi function may analogously be defined for any pair of conjugated variables. In analysis of time varying signals these variables are time and frequency. In this paper we consider Husimi function in time-frequency space, we derive some properties of the function and give time-frequency analysis of some characteristic signals., U ovom radu razmotrena je Husimijeva funkcija na prostoru kanonski spregnutih promenljivih vreme-frekvencija. Izvedene su neke njene nove osobine koje su ilustrovane na nekoliko analitički zadatih signala. Pokazano je da se Husimijeva funkcija može koristiti pri vremensko-frekvencijskoj analizi signala.",
journal = "Tehnika",
title = "Use of Husimi function in time frequency signal analysis, Primena Husimijeve funkcije u vremensko-frekvencijskoj analizi signala",
volume = "68",
number = "5",
pages = "905-909",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10951"
}

Davidović, M. D., Davidović, M. D.,& Srećković, M.. (2013). Use of Husimi function in time frequency signal analysis. in Tehnika, 68(5), 905-909.
https://hdl.handle.net/21.15107/rcub_vinar_10951

Davidović MD, Davidović MD, Srećković M. Use of Husimi function in time frequency signal analysis. in Tehnika. 2013;68(5):905-909.
https://hdl.handle.net/21.15107/rcub_vinar_10951 .

Davidović, Miloš D., Davidović, Milena D., Srećković, Milesa, "Use of Husimi function in time frequency signal analysis" in Tehnika, 68, no. 5 (2013):905-909,
https://hdl.handle.net/21.15107/rcub_vinar_10951 .

TY  - JOUR
AU  - Andreev, V. A.
AU  - Davidović, Dragomir M.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena D.
AU  - Man'ko, V. I.
AU  - Man'ko, M. A.
PY  - 2011
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4443
AB  - We consider the Husimi Q-functions, which are quantum quasiprobability distributions in the phase space, and investigate their transformation properties under a scale transformation (q, p) - GT (lambda q, lambda p). We prove a theorem that under this transformation, the Husimi function of a physical state is transformed into a function that is also a Husimi function of some physical state. Therefore, the scale transformation defines a positive map of density operators. We investigate the relation of Husimi functions to Wigner functions and symplectic tomograms and establish how they transform under the scale transformation. As an example, we consider the harmonic oscillator and show how its states transform under the scale transformation.
T2  - Theoretical and Mathematical Physics
T1  - A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms
VL  - 166
IS  - 3
SP  - 356
EP  - 368
DO  - 10.1007/s11232-011-0028-8
ER  - 

@article{
author = "Andreev, V. A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena D. and Man'ko, V. I. and Man'ko, M. A.",
year = "2011",
abstract = "We consider the Husimi Q-functions, which are quantum quasiprobability distributions in the phase space, and investigate their transformation properties under a scale transformation (q, p) - GT (lambda q, lambda p). We prove a theorem that under this transformation, the Husimi function of a physical state is transformed into a function that is also a Husimi function of some physical state. Therefore, the scale transformation defines a positive map of density operators. We investigate the relation of Husimi functions to Wigner functions and symplectic tomograms and establish how they transform under the scale transformation. As an example, we consider the harmonic oscillator and show how its states transform under the scale transformation.",
journal = "Theoretical and Mathematical Physics",
title = "A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms",
volume = "166",
number = "3",
pages = "356-368",
doi = "10.1007/s11232-011-0028-8"
}

Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M. D., Man'ko, V. I.,& Man'ko, M. A.. (2011). A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms. in Theoretical and Mathematical Physics, 166(3), 356-368.
https://doi.org/10.1007/s11232-011-0028-8

Andreev VA, Davidović DM, Davidović LD, Davidović MD, Man'ko VI, Man'ko MA. A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms. in Theoretical and Mathematical Physics. 2011;166(3):356-368.
doi:10.1007/s11232-011-0028-8 .

Andreev, V. A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milena D., Man'ko, V. I., Man'ko, M. A., "A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms" in Theoretical and Mathematical Physics, 166, no. 3 (2011):356-368,
https://doi.org/10.1007/s11232-011-0028-8 . .

TY  - JOUR
AU  - Andreev, V. A.
AU  - Davidović, Dragomir M.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena D.
PY  - 2011
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6898
AB  - Husimi Q-functions are the only functions from the class of Cohen quasi-distributions on phase space that after scaling transformation (q, p) - GT (lambda q, lambda p) remain in the same class when the modulus of the scaling parameter is smaller than unity and so, in this case, describe a physical state. We found the Wigner functions and symplectic tomograms of such states. We applied the obtained general results to the Fock states of the harmonic oscillator.
T2  - Physica Scripta
T1  - Relations between scaling-transformed Husimi functions, Wigner functions and symplectic tomograms describing corresponding physical states
VL  - T143
DO  - 10.1088/0031-8949/2011/T143/014003
ER  - 

@article{
author = "Andreev, V. A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena D.",
year = "2011",
abstract = "Husimi Q-functions are the only functions from the class of Cohen quasi-distributions on phase space that after scaling transformation (q, p) - GT (lambda q, lambda p) remain in the same class when the modulus of the scaling parameter is smaller than unity and so, in this case, describe a physical state. We found the Wigner functions and symplectic tomograms of such states. We applied the obtained general results to the Fock states of the harmonic oscillator.",
journal = "Physica Scripta",
title = "Relations between scaling-transformed Husimi functions, Wigner functions and symplectic tomograms describing corresponding physical states",
volume = "T143",
doi = "10.1088/0031-8949/2011/T143/014003"
}

Andreev, V. A., Davidović, D. M., Davidović, L. D.,& Davidović, M. D.. (2011). Relations between scaling-transformed Husimi functions, Wigner functions and symplectic tomograms describing corresponding physical states. in Physica Scripta, T143.
https://doi.org/10.1088/0031-8949/2011/T143/014003

Andreev VA, Davidović DM, Davidović LD, Davidović MD. Relations between scaling-transformed Husimi functions, Wigner functions and symplectic tomograms describing corresponding physical states. in Physica Scripta. 2011;T143.
doi:10.1088/0031-8949/2011/T143/014003 .

Andreev, V. A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milena D., "Relations between scaling-transformed Husimi functions, Wigner functions and symplectic tomograms describing corresponding physical states" in Physica Scripta, T143 (2011),
https://doi.org/10.1088/0031-8949/2011/T143/014003 . .

TY  - JOUR
AU  - Davidović, Ljubica
AU  - Arsenović, Dušan
AU  - Davidović, Milena D.
AU  - Davidović, Dragomir M.
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3706
AB  - Using the resolution of identity spanned by coherent states of the harmonic oscillator, any entire function of the creation and the annihilation operators and its action on a vector in Hilbert space can be defined directly and simply. We show that such a direct approach applied to non-entire functions ln (a) over cap and ln (a) over cap (dagger), present in the literature, may lead to errors and contradictions. We elucidate their roots and propose a way to avoid them. We discuss the obtained results.
T2  - Journal of Physics. A: Mathematical and Theoretical
T1  - Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them
VL  - 42
IS  - 23
DO  - 10.1088/1751-8113/42/23/235302
ER  - 

@article{
author = "Davidović, Ljubica and Arsenović, Dušan and Davidović, Milena D. and Davidović, Dragomir M.",
year = "2009",
abstract = "Using the resolution of identity spanned by coherent states of the harmonic oscillator, any entire function of the creation and the annihilation operators and its action on a vector in Hilbert space can be defined directly and simply. We show that such a direct approach applied to non-entire functions ln (a) over cap and ln (a) over cap (dagger), present in the literature, may lead to errors and contradictions. We elucidate their roots and propose a way to avoid them. We discuss the obtained results.",
journal = "Journal of Physics. A: Mathematical and Theoretical",
title = "Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them",
volume = "42",
number = "23",
doi = "10.1088/1751-8113/42/23/235302"
}

Davidović, L., Arsenović, D., Davidović, M. D.,& Davidović, D. M.. (2009). Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them. in Journal of Physics. A: Mathematical and Theoretical, 42(23).
https://doi.org/10.1088/1751-8113/42/23/235302

Davidović L, Arsenović D, Davidović MD, Davidović DM. Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them. in Journal of Physics. A: Mathematical and Theoretical. 2009;42(23).
doi:10.1088/1751-8113/42/23/235302 .

Davidović, Ljubica, Arsenović, Dušan, Davidović, Milena D., Davidović, Dragomir M., "Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them" in Journal of Physics. A: Mathematical and Theoretical, 42, no. 23 (2009),
https://doi.org/10.1088/1751-8113/42/23/235302 . .

TY  - CONF
AU  - Davidović, Milena D.
AU  - Arsenović, Dušan
AU  - Davidović, Dragomir M.
PY  - 2006
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6620
AB  - On the coherent states vertical bar alpha GT any entire function of creation and annihilation operators may be defined. We show that it is not the case for non-entire functions. Use of vertical bar alpha GT LT alpha vertical bar as identity operator for a non-entire function may lead to contradictory results. On the example of the phase operator we show how these possible contradictions may be avoided. On the coherent states |alpha GT any entire function of creation and annihilation operators may be defined. We show that it is not the case for non-entire functions. Use of |alpha GT LT alpha| as identity operator for a non-entire function may lead to contradictory results. On the example of the phase operator we show how these possible contradictions may be avoided.
C3  - Journal of Physics: Conference Series
T1  - Non-entire functions of creation and annihilation operators and their relation to phase operator
VL  - 36
SP  - 46
EP  - +
DO  - 10.1088/1742-6596/36/1/009
ER  - 

@conference{
author = "Davidović, Milena D. and Arsenović, Dušan and Davidović, Dragomir M.",
year = "2006",
abstract = "On the coherent states vertical bar alpha GT any entire function of creation and annihilation operators may be defined. We show that it is not the case for non-entire functions. Use of vertical bar alpha GT LT alpha vertical bar as identity operator for a non-entire function may lead to contradictory results. On the example of the phase operator we show how these possible contradictions may be avoided. On the coherent states |alpha GT any entire function of creation and annihilation operators may be defined. We show that it is not the case for non-entire functions. Use of |alpha GT LT alpha| as identity operator for a non-entire function may lead to contradictory results. On the example of the phase operator we show how these possible contradictions may be avoided.",
journal = "Journal of Physics: Conference Series",
title = "Non-entire functions of creation and annihilation operators and their relation to phase operator",
volume = "36",
pages = "46-+",
doi = "10.1088/1742-6596/36/1/009"
}

Davidović, M. D., Arsenović, D.,& Davidović, D. M.. (2006). Non-entire functions of creation and annihilation operators and their relation to phase operator. in Journal of Physics: Conference Series, 36, 46-+.
https://doi.org/10.1088/1742-6596/36/1/009

Davidović MD, Arsenović D, Davidović DM. Non-entire functions of creation and annihilation operators and their relation to phase operator. in Journal of Physics: Conference Series. 2006;36:46-+.
doi:10.1088/1742-6596/36/1/009 .

Davidović, Milena D., Arsenović, Dušan, Davidović, Dragomir M., "Non-entire functions of creation and annihilation operators and their relation to phase operator" in Journal of Physics: Conference Series, 36 (2006):46-+,
https://doi.org/10.1088/1742-6596/36/1/009 . .

TY  - CONF
AU  - Vukanić, Jovan V.
AU  - Davidović, Milena D.
AU  - Arsenović, Dušan
AU  - Davidović, Dragomir M.
PY  - 2006
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6635
AB  - The results obtained in a Monte Carlo simulation of X-ray reflection from water show that for energies up to 20 keV, single and double reflected photons absolutely dominate. Analyzing in detail geometry of the collisions and corresponding energy relations we derive analytically the energy and angular distributions of reflected photons in double collision approximation. The results of the two approaches are compared and discussed. (c) 2006 Elsevier Ltd. All rights reserved.
C3  - Radiation Physics and Chemistry
T1  - Energy distribution of X-rays reflected from a half space in double collision approximation
VL  - 75
IS  - 11
SP  - 1953
EP  - 1955
DO  - 10.1016/j.radphyschem.2005.07.046
ER  - 

@conference{
author = "Vukanić, Jovan V. and Davidović, Milena D. and Arsenović, Dušan and Davidović, Dragomir M.",
year = "2006",
abstract = "The results obtained in a Monte Carlo simulation of X-ray reflection from water show that for energies up to 20 keV, single and double reflected photons absolutely dominate. Analyzing in detail geometry of the collisions and corresponding energy relations we derive analytically the energy and angular distributions of reflected photons in double collision approximation. The results of the two approaches are compared and discussed. (c) 2006 Elsevier Ltd. All rights reserved.",
journal = "Radiation Physics and Chemistry",
title = "Energy distribution of X-rays reflected from a half space in double collision approximation",
volume = "75",
number = "11",
pages = "1953-1955",
doi = "10.1016/j.radphyschem.2005.07.046"
}

Vukanić, J. V., Davidović, M. D., Arsenović, D.,& Davidović, D. M.. (2006). Energy distribution of X-rays reflected from a half space in double collision approximation. in Radiation Physics and Chemistry, 75(11), 1953-1955.
https://doi.org/10.1016/j.radphyschem.2005.07.046

Vukanić JV, Davidović MD, Arsenović D, Davidović DM. Energy distribution of X-rays reflected from a half space in double collision approximation. in Radiation Physics and Chemistry. 2006;75(11):1953-1955.
doi:10.1016/j.radphyschem.2005.07.046 .

Vukanić, Jovan V., Davidović, Milena D., Arsenović, Dušan, Davidović, Dragomir M., "Energy distribution of X-rays reflected from a half space in double collision approximation" in Radiation Physics and Chemistry, 75, no. 11 (2006):1953-1955,
https://doi.org/10.1016/j.radphyschem.2005.07.046 . .