Complexifier Versus Factorization and Deformation Methods For Generation of Coherent States of a 1D NLHO: I. Mathematical Construction

TL;DR

This paper compares three mathematical methods—complexifier, factorization, and deformation—for constructing coherent states of a one-dimensional nonlinear harmonic oscillator, and provides an exact solution using Jacobi polynomials.

Contribution

It introduces a comprehensive comparison of three methods for coherent state construction and derives an exact Schrödinger solution for the 1D NLHO using Jacobi polynomials.

Findings

All three methods successfully construct coherent states.

The exact Schrödinger solution is expressed in terms of Jacobi polynomials.

Bridging the methods enhances understanding of nonlinear quantum systems.

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 $P_n^{a,b}$'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.