Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory

TL;DR

This paper investigates the eigenvalues and eigenfunctions of a harmonic oscillator on a noncommutative two-dimensional lattice, extending quantum mechanics to noncommutative geometry and analyzing thermodynamic properties.

Contribution

It introduces a method to compute eigenvalues and eigenfunctions for noncommutative lattice oscillators, advancing understanding of quantum systems in noncommutative spaces.

Findings

Eigenvalues and eigenfunctions derived for noncommutative harmonic oscillator

Thermodynamic properties analyzed in both commutative and noncommutative cases

Extension of quantum mechanics framework to noncommutative lattice models

Abstract

Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding Hamiltonian. First we consider the case of ordinary quantum mechanics, and we point out the thermodynamic properties of the model. Then we consider the same question when both coordinates and momentums are noncommutative.