Perturbative Aspects of q-Deformed Dynamics

TL;DR

This paper explores the perturbative features of q-deformed quantum mechanics, analyzing how q-deformation influences the Schrödinger equation and introduces momentum-dependent interactions, with specific examples involving harmonic and Morse potentials.

Contribution

It provides a detailed perturbative analysis of q-deformed quantum mechanics and introduces new representations of q-deformed interactions in two different approaches.

Findings

q-deformed Schrödinger equation exhibits additional momentum-dependent interactions

Representations of these interactions are developed in two approaches

Examples include modifications to harmonic-oscillator and Morse potentials

Abstract

Within the framework of the q-deformed Heisenberg algebra a dynamical equation of q-deformed quantum mechanics is discussed. The perturbative aspects of the q-deformed Schr\"odinger equation are analyzed. General representations of the additional momentum-dependent interaction originating from the q-deformed effects are presented in two approaches. As examples, such additional interactions related to the harmonic-oscillator potential and the Morse potential are demonstrated.