Coherent States for the Non-Linear Harmonic Oscillator

TL;DR

This paper explores the properties of coherent states in a quantum non-linear harmonic oscillator, showing they closely resemble classical oscillations and maintain stable uncertainty relations.

Contribution

It introduces a generalized coherent state framework for the quantum non-linear oscillator and analyzes its classical-like behavior and quantum features.

Findings

Position expectation oscillates harmonically

Uncertainty relations remain time-independent

Features like squeezed states are discussed

Abstract

Wave packets for the Quantum Non-Linear Oscillator are considered in the Generalized Coherent State framerwork. To first order in the non-linearity parameter the Coherent State behaves very similarly to its classical counterpart. The position expectation value oscillates in a simple harmonic manner. The energy-momentum uncertainty relation is time independent as in a harmonic oscillator. Various features, (such as the Squeezed State nature), of the Coherent State have been discussed.