Quantum Difference Problem with Point Interaction

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.

Keywords

• q-difference equation
• Jost solution
• point interaction
• spectral analysis

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