Complexifier versus factorization and deformation methods for generation of coherent states of a 1D NLHO I. Mathematical construction

Abstract

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 na,b,s, bridging the difference between them is possible, we give here also the exact solution of Schrödinger equation of 1D NLHO in terms of Jacobi polynomials. © World Scientific Publishing Company.