Phase coherent states with circular Jacobi polynomials for the pseudoharmonic oscillator

TL;DR

This paper introduces a new class of phase coherent states for the pseudoharmonic oscillator using circular Jacobi polynomials, generalizing known phase states and providing explicit wavefunctions and transformations.

Contribution

It constructs generalized phase coherent states with circular Jacobi polynomial coefficients, extending existing phase states and analyzing their properties for the pseudoharmonic oscillator.

Findings

States form a resolution of the identity in the limit epsilon to 0+

Closed-form wavefunctions derived for specific parameter values

Transform associated with the coherent states defined and analyzed

Abstract

We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states by circular Jacobi polynomials with parameter "gamma". The special case "gamma" = 0 corresponds to well known phase coherent phase states. The constructed states are superposition of eigenstates of a one-parameter pseudoharmonic oscillator depending on "alpha" and solve the identity of the state Hilbert space at the limit "epsilon"->0+. Closed form for their wavefunctions are obtained in the case "alpha" = "gamma" + 1 and their associated coherent states transform is defined.