New SU(1, 1) Position-Dependent Effective Mass Coherent States for the Generalized Shifted Harmonic Oscillator

TL;DR

This paper introduces a new class of SU(1, 1) position-dependent effective mass coherent states for the shifted harmonic oscillator, demonstrating their algebraic structure, minimized uncertainty, and classical-like dynamical behavior.

Contribution

It constructs novel PDEM coherent states using a similarity transformation and Lie algebra techniques, extending the understanding of coherent states in position-dependent mass systems.

Findings

PDEM CS form an SU(1, 1) Lie algebra basis

Uncertainty in PDEM CS is minimized

Probability density exhibits classical wave packet oscillations

Abstract

A new SU(1, 1) position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator algebra (GDOA) generators for PDEM system and construct a new set of operators which close the su(1, 1) Lie algebra, being the PDEM CS of the basis for its unitary irreducible representation. The residual potential is associated to the SHO. From the Lie algebra generators, we evaluate the uncertainty relationship for a position and momentum-like operators in the PDEM CS and show that it is minimized in the sense of Barut-Girardello CS. We prove that the deduced PDEM CS preserve the same analytical form than those of Glauber states. We show that the probability density of dynamical evolution in the PDEM CS oscillates back and forth as time goes by and behaves as classical wave packet.