COMPLEXIFIER VERSUS FACTORIZATION AND DEFORMATION METHODS FOR GENERATION OF COHERENT STATES OF A 1D NLHO I: MATHEMATICAL CONSTRUCTION

Three methods: complexifier, factorization and deformation, for construction of coherent states are presented for one-dimensional nonlinear harmonic oscillator (1D NLHO). Since by exploring the Jacobi polynomials , bridging the difference between them is possible, we give here also the exact solution of Schrodinger equation of 1D NLHO in terms of Jacobi polynomials.