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 Pa,bn ’s, bridging the difference between them is possible, we give here also the exact solution of Schr¨odinger equation of 1D NLHO in terms of Jacobi polynomials