TY  - JOUR
AU  - Topalović, Dušan
AU  - Arsoski, Vladimir
AU  - Pavlović, Suncan
AU  - Čukarić, Nemanja A. 
AU  - Tadić, Milan Ž.
AU  - Peeters, François M.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/974
AB  - We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N-2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrodinger equation.
T2  - Communications in Theoretical Physics
T1  - On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires
VL  - 65
IS  - 1
SP  - 105
EP  - 113
UR  - https://hdl.handle.net/21.15107/rcub_vinar_974
ER  - 

@article{
author = "Topalović, Dušan and Arsoski, Vladimir and Pavlović, Suncan and Čukarić, Nemanja A.  and Tadić, Milan Ž. and Peeters, François M.",
year = "2016",
abstract = "We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N-2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrodinger equation.",
journal = "Communications in Theoretical Physics",
title = "On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires",
volume = "65",
number = "1",
pages = "105-113",
url = "https://hdl.handle.net/21.15107/rcub_vinar_974"
}

Topalović, D., Arsoski, V., Pavlović, S., Čukarić, N. A., Tadić, M. Ž.,& Peeters, F. M.. (2016). On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires. in Communications in Theoretical Physics, 65(1), 105-113.
https://hdl.handle.net/21.15107/rcub_vinar_974

Topalović D, Arsoski V, Pavlović S, Čukarić NA, Tadić MŽ, Peeters FM. On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires. in Communications in Theoretical Physics. 2016;65(1):105-113.
https://hdl.handle.net/21.15107/rcub_vinar_974 .

Topalović, Dušan, Arsoski, Vladimir, Pavlović, Suncan, Čukarić, Nemanja A. , Tadić, Milan Ž., Peeters, François M., "On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrodinger Equation for Interdiffused Quantum Wells and Quantum Wires" in Communications in Theoretical Physics, 65, no. 1 (2016):105-113,
https://hdl.handle.net/21.15107/rcub_vinar_974 .