Eigenfunction expansions in the imaginary Lobachevsky space

TL;DR

This paper investigates eigenfunctions of the Schrödinger equation with Coulomb potential in imaginary Lobachevsky space, providing solutions in hypergeometric functions, normalization, and expansion coefficients.

Contribution

It introduces explicit eigenfunction solutions in hypergeometric functions for Coulomb problems in imaginary Lobachevsky space, including normalization and expansion coefficients.

Findings

Derived eigenfunctions in hypergeometric form

Established normalization constants

Calculated mutual expansion coefficients

Abstract

Eigenfunctions of the Schrodinger equation with the Coulomb potential in the imaginary Lobachevsky space are studied in two coordinate systems admitting solutions in terms of hypergeometric functions. Normalization and coefficients of mutual expansions for some sets of solutions are found.