Phase coherent states with circular Jacobi polynomials for the pseudoharmonic oscillator

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.