Coherent states for polynomial su(1,1) algebra and a conditionally solvable system

TL;DR

This paper develops a new class of coherent states for polynomial su(1,1) algebra, extending previous work on deformed su(2) algebra, and applies these states to a conditionally solvable radial oscillator system.

Contribution

It introduces a discrete class of coherent states for polynomial su(1,1) algebra, unifying and extending existing coherent state sets, and constructs states for a related cubic algebra.

Findings

Constructed discrete representations of nonlinearly deformed su(1,1) algebra.

Extended the coherent state construction to include Barut-Girardello and Perelomov types.

Applied the framework to a conditionally solvable radial oscillator problem.

Abstract

In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1,1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1,1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.