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 $P_n^{a,b}$'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.