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

While dealing with the J -matrix method for the harmonic oscillator to write down its tridiagonal matrix representation in an orthonormal basis of L 2 ( R ) , we rederive a set of generalized coherent states (GCS) of Perelomov type labelled by points z of the complex plane C and depending on an integer number m ∈ Z + . The number states expansion of these GCS gives rise to coefficients that are complex Hermite polynomials and whose linear superpositions provide eigenfunctions for the two-dimensional magnetic Laplacian, associated with the m th Landau level. We further generalize this construction to the Morse oscillator by introducing a new set of Glauber-type GCS.