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 languageEnglish
Title of host publicationProceedings of the International Conference Days on Diffraction 2017, DD 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781538647967
Publication statusPublished - 5 Dec 2017
Event2017 International Conference Days on Diffraction, DD 2017 - St. Petersburg
Duration: 18 Jun 201722 Jun 2017


Conference2017 International Conference Days on Diffraction, DD 2017
CountryRussian Federation
CitySt. Petersburg

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

Fingerprint Dive into the research topics of 'New representations for square-integrable spheroidal functions'. Together they form a unique fingerprint.

Cite this