Quantum Difference Problem with Point Interaction

AYGAR KÜÇÜKEVCİLİOĞLU Y., ÖZBEY G. G., ÖZNUR G. B.

Konuralp Journal of Mathematics, vol.11, no.2, pp.218-228, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2023
  • Journal Name: Konuralp Journal of Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.218-228
  • Keywords: Jost solution, point interaction, q-difference equation, spectral analysis
  • Ankara University Affiliated: Yes

Abstract

The main aim of this study is to examine the spectral analysis of q-difference equation with point interaction. We first find Jost solution and Jost function of this problem. Next, we establish the resolvent operator, continuous spectrum and discrete spectrum of the problem. At last, we demonstrate that the quantum boundary value problem with point interaction has finite number of eigenvalues and spectral singularities with finite multiplicities under certain conditions.