Generalized coherent states for the harmonic oscillator by the J-matrix method with an extension to the Morse potential

TL;DR

This paper develops generalized coherent states for the harmonic oscillator using the J-matrix method and extends the approach to the Morse potential, providing new eigenfunctions and state representations.

Contribution

It introduces a novel set of generalized coherent states for both harmonic and Morse oscillators using the J-matrix method, linking them to complex Hermite polynomials and magnetic Laplacian eigenfunctions.

Findings

Derived GCS of Perelomov type for the harmonic oscillator.

Expressed GCS coefficients as complex Hermite polynomials.

Extended the GCS framework to the Morse oscillator.

Abstract

While dealing with the J-Matrix method for the harmonic oscillator to write down its tridiagonal matrix representation in an orthonormal basis of L2(R); we rederive a set of generalized coherent states (GCS) of Perelomov type labeled by points z of the complex plane C and depending on a positive integer number m The number states expansion of these GCS gives rise to coefficients that are complex Hermite polynomials whose linear superpositions provide eigenfunctions for the two-dimensional magnetic Laplacian associated with the mth Landau level. We extend this procedure to the Morse oscillator by constructing a new set of GCS of Glauber type.