2024/12/04 by Hashim A. Yamani, Yamani, Hashim A., Zouhaı̈r Mouayn +1 · 1 citation
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Mechanical and Optical Resonators #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2412.02958
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.