New representations for square-integrable spheroidal functions

V. N. Kovalenko; A. M. Puchkov

doi:10.1109/DD.2017.8168021

New representations for square-integrable spheroidal functions

Research output › › peer-review

Abstract

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.

Original language	English
Title of host publication	Proceedings of the International Conference Days on Diffraction 2017, DD 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	189-193
Number of pages	5
Volume	2017-December
ISBN (Electronic)	9781538647967
DOIs	https://doi.org/10.1109/DD.2017.8168021
Publication status	Published - 5 Dec 2017
Event	2017 International Conference Days on Diffraction, DD 2017 - St. Petersburg Duration: 18 Jun 2017 → 22 Jun 2017

Conference

Conference	2017 International Conference Days on Diffraction, DD 2017
Country	Russian Federation
City	St. Petersburg
Period	18/06/17 → 22/06/17

Scopus subject areas

Acoustics and Ultrasonics
Surfaces and Interfaces
Radiation
Electronic, Optical and Magnetic Materials
Electrical and Electronic Engineering
Physics and Astronomy (miscellaneous)
Mathematical Physics

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10.1109/DD.2017.8168021

http://www.scopus.com/inward/record.url?scp=85045986420&partnerID=8YFLogxK

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Cite this

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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",

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language = "English",

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pages = "189--193",

booktitle = "Proceedings of the International Conference Days on Diffraction 2017, DD 2017",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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note = "2017 International Conference Days on Diffraction, DD 2017 ; Conference date: 18-06-2017 Through 22-06-2017",

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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, 18/06/17. https://doi.org/10.1109/DD.2017.8168021

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

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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 -