Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
New representations for square-integrable spheroidal functions. / Kovalenko, V. N.; Puchkov, A. M.
Proceedings of the International Conference Days on Diffraction 2017, DD 2017. Том 2017-December Institute of Electrical and Electronics Engineers Inc., 2017. стр. 189-193.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - New representations for square-integrable spheroidal functions
AU - Kovalenko, V. N.
AU - Puchkov, A. M.
PY - 2017/12/5
Y1 - 2017/12/5
N2 - We discuss the solution of boundary value problems that arise after the separation of variables in the Schrödinger equation in oblate spheroidal coordinates. The specificity of these boundary value problems is that the singular points of the differential equation are outside the region in which the eigenfunctions are considered. This prevents the construction of eigenfunctions as a convergent series. To solve this problem, we generalize and apply the Jaffe transformation. We find the solution of the problem as trigonometric and power series in the particular case when the charge parameter is zero. Application of the obtained results to the spectral problem for the model of a quantum ring in the form of a potential well of a spheroidal shape is discussed with introducing a potential well of a finite depth.
AB - We discuss the solution of boundary value problems that arise after the separation of variables in the Schrödinger equation in oblate spheroidal coordinates. The specificity of these boundary value problems is that the singular points of the differential equation are outside the region in which the eigenfunctions are considered. This prevents the construction of eigenfunctions as a convergent series. To solve this problem, we generalize and apply the Jaffe transformation. We find the solution of the problem as trigonometric and power series in the particular case when the charge parameter is zero. Application of the obtained results to the spectral problem for the model of a quantum ring in the form of a potential well of a spheroidal shape is discussed with introducing a potential well of a finite depth.
KW - Eigenvalues and eigenfunctions
KW - Mathematical model
KW - Boundary value problems
KW - Quantum mechanics
KW - Schrodinger equation
KW - differential equation
KW - spheroidal shape
KW - spectral problem
UR - http://www.scopus.com/inward/record.url?scp=85045986420&partnerID=8YFLogxK
U2 - 10.1109/DD.2017.8168021
DO - 10.1109/DD.2017.8168021
M3 - Conference contribution
AN - SCOPUS:85045986420
VL - 2017-December
SP - 189
EP - 193
BT - Proceedings of the International Conference Days on Diffraction 2017, DD 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 International Conference Days on Diffraction, DD 2017
Y2 - 18 June 2017 through 22 June 2017
ER -
ID: 25865583