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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.
Язык оригинала | английский |
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Название основной публикации | Proceedings of the International Conference Days on Diffraction 2017, DD 2017 |
Издатель | Institute of Electrical and Electronics Engineers Inc. |
Страницы | 189-193 |
Число страниц | 5 |
Том | 2017-December |
ISBN (электронное издание) | 9781538647967 |
DOI | |
Состояние | Опубликовано - 5 дек 2017 |
Событие | 2017 International Conference Days on Diffraction, DD 2017 - St. Petersburg, Российская Федерация Продолжительность: 18 июн 2017 → 22 июн 2017 |
конференция | 2017 International Conference Days on Diffraction, DD 2017 |
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Страна/Tерритория | Российская Федерация |
Город | St. Petersburg |
Период | 18/06/17 → 22/06/17 |
ID: 25865583