Subtle inconsistencies in the straightforward definition of the logarithmic function of annihilation and creation operators and a way to avoid them
Апстракт
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.
Извор:
Journal of Physics. A: Mathematical and Theoretical, 2009, 42, 23Финансирање / пројекти:
- Ministry of Science and Environment Protection of the Republic of Serbia [141041G, 141003, 141036]
DOI: 10.1088/1751-8113/42/23/235302
ISSN: 1751-8113
WoS: 000266287500011
Scopus: 2-s2.0-70449506537
Колекције
Институција/група
VinčaTY - 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 . .