Nilpotent Morse algebra and time evolution of certain associated coherent states

TL;DR

This paper studies the time evolution of coherent states in various systems, highlighting the Morse system's algebraic structure and proposing a new way to construct Morse oscillator coherent states.

Contribution

It introduces a nilpotent Morse algebra within the generalized Heisenberg algebra framework and constructs coherent states for the Morse oscillator.

Findings

Identifies parameter regions where systems behave classically

Shows Morse system is described by a nilpotency condition

Proposes a new construction method for Morse oscillator coherent states

Abstract

We provide the time evolutions of the linear and nonlinear coherent states for several systems characterized by different energy spectra, and we identify the regions in the parameter space where these systems behave closer to the classical systems. The Morse system is algebraically found within the frame of generalized Heisenberg algebra(GHA). We demonstrate that this system is described by a nilpotency condition. Then, we propose a construction of coherent states for the Morse oscillator.