Approximate coherent states for nonlinear systems

TL;DR

This paper develops nonlinear coherent states for specific quantum systems using f-deformed oscillator formalism, analyzing their properties as deformed annihilation and displacement operator states, with applications to Morse and P"oschl-Teller potentials.

Contribution

It introduces a method to construct nonlinear coherent states for systems with linear and quadratic Hamiltonian terms using two definitions, expanding the understanding of such states in quantum systems.

Findings

Nonlinear coherent states exhibit unique occupation number distributions.

Phase space evolution of these states reveals distinctive dynamics.

Uncertainty relations are analyzed for the constructed states.

Abstract

On the basis of the f-deformed oscillator formalism, we propose to construct nonlinear coherent states for Hamiltonian systems having linear and quadratic terms in the the number operator by means of the two following definitions: i) as deformed annihilation operator coherent states (AOCS) and ii) as deformed displacement operator coherent states (DOCS). For the particular cases of the Morse and Modified P\"oschl-Teller potentials, modeled as f-deformed oscillators (both supporting a finite number of bound states), the properties of their corresponding nonlinear coherent states, viewed as DOCS, are analyzed in terms of their occupation number distribution, their evolution on phase space, and their uncertainty relations.