A General Scheme for Construction of Coherent States of Anharmonic Oscillators

TL;DR

This paper introduces a unified algebraic method for constructing coherent states of various anharmonic oscillators, extending known states and discovering new ones, with applications in supersymmetric quantum mechanics.

Contribution

It presents a novel supersymmetric-algebraic approach capable of generating both known and new coherent states for multiple anharmonic oscillators.

Findings

Generated coherent states for Morse, Wei Hua, Kratzer-Fues oscillators

Discovered new coherent states for generalized Morse and Kratzer-Fues oscillators

Method facilitates deriving superpotentials for SUSYQM

Abstract

A mixed supersymmetric-algebraic approach to construction of the minimum uncertainty coherent states of anharmonic oscillators is presented. It permits generating not only the well-known coherent states of the harmonic and Morse oscillators but also the so far unknown coherent states of the Wei Hua, Kratzer-Fues and generalized Morse and Kratzer-Fues oscillators. The method can be applied also to generate superpotentials indispensable for deriving the Schr\"odinger equation in the supersymmetric form amenable to direct solution in the SUSYQM scheme.