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

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.

12 pages

References in corpus (7)

• Noncommutative oscillator, symmetry and Landau problem
• Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian
• Phase-space noncommutative formulation of Ozawa's uncertainty principle
• Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
• Quantum engines and the range of the second law of thermodynamics in the noncommutative phase-space
• Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices
• Thermodynamics of a charged particle in a noncommutative plane in a background magnetic field