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New representations for square-integrable spheroidal functions. / Kovalenko, V. N.; Puchkov, A. M.

Proceedings of the International Conference Days on Diffraction 2017, DD 2017. Vol. 2017-December Institute of Electrical and Electronics Engineers Inc., 2017. p. 189-193.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Kovalenko, VN & Puchkov, AM 2017, New representations for square-integrable spheroidal functions. in Proceedings of the International Conference Days on Diffraction 2017, DD 2017. vol. 2017-December, Institute of Electrical and Electronics Engineers Inc., pp. 189-193, 2017 International Conference Days on Diffraction, DD 2017, St. Petersburg, Russian Federation, 18/06/17. https://doi.org/10.1109/DD.2017.8168021

APA

Kovalenko, V. N., & Puchkov, A. M. (2017). New representations for square-integrable spheroidal functions. In Proceedings of the International Conference Days on Diffraction 2017, DD 2017 (Vol. 2017-December, pp. 189-193). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD.2017.8168021

Vancouver

Kovalenko VN, Puchkov AM. New representations for square-integrable spheroidal functions. In Proceedings of the International Conference Days on Diffraction 2017, DD 2017. Vol. 2017-December. Institute of Electrical and Electronics Engineers Inc. 2017. p. 189-193 https://doi.org/10.1109/DD.2017.8168021

Author

Kovalenko, V. N. ; Puchkov, A. M. / New representations for square-integrable spheroidal functions. Proceedings of the International Conference Days on Diffraction 2017, DD 2017. Vol. 2017-December Institute of Electrical and Electronics Engineers Inc., 2017. pp. 189-193

BibTeX

@inproceedings{a961a8f6068648c5b53f2a416ad1286b,
title = "New representations for square-integrable spheroidal functions",
abstract = "We discuss the solution of boundary value problems that arise after the separation of variables in the Schr{\"o}dinger 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.",
keywords = "Eigenvalues and eigenfunctions, Mathematical model, Boundary value problems, Quantum mechanics, Schrodinger equation, differential equation, spheroidal shape, spectral problem",
author = "Kovalenko, {V. N.} and Puchkov, {A. M.}",
year = "2017",
month = dec,
day = "5",
doi = "10.1109/DD.2017.8168021",
language = "English",
volume = "2017-December",
pages = "189--193",
booktitle = "Proceedings of the International Conference Days on Diffraction 2017, DD 2017",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",
note = "2017 International Conference Days on Diffraction, DD 2017 ; Conference date: 18-06-2017 Through 22-06-2017",

}

RIS

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