Lie Algebra Contractions and Interbasis Expansions on Two-Dimensional Hyperboloid IIB. Non-Subgroup Basis

TL;DR

This paper explores solutions of the Laplace-Beltrami equation on a two-sheeted hyperboloid in three non-subgroup coordinate systems, computes interbasis expansion coefficients, and demonstrates a contraction to Euclidean plane eigenfunctions.

Contribution

It introduces a contraction procedure for eigenfunctions from hyperboloid to Euclidean plane across multiple non-subgroup coordinate systems.

Findings

Explicit interbasis expansion coefficients are calculated.

A contraction method from hyperboloid to Euclidean plane is developed.

Solutions are provided for three non-subgroup coordinate systems.

Abstract

The paper describes solutions of the Laplace-Beltrami equation on two-dimensional two-sheeted hyperboloid for three non-subgroup coordinate systems: semi-sircular parabolic, elliptic parabolic and hyperbolic parabolic. The coefficients of interbasis expansions of solutions in the specified coordinate systems through some subgroup bases are calculated. A contraction procedure for all normalized eigenfunctions in three non-subgroup coordinate systems from the hyperboloid to the Euclidean plane is realized.