Antonin Danvidé Kanfon

arXiv2019

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

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.

hep-th↗

arXiv2016

Spherically symmetric potential in noncommutative spacetime with a compactified extra dimensions

The Schrödinger equation of the spherical symmetry quantum models such as the hydrogen atom problem seems to be analytically non-solvable in higher dimensions. When we try to compactifying one or several dimensions this question can maybe solved. This paper stands for the study of the spherical symmetry quantum models on noncommutative spacetime with compactified extra dimensions. We provide analytically the resulting spectrum of the hydrogen atom and Yukawa problem in $4+1$ dimensional noncommutative spacetime in the first order approximation of noncommutative parameter. The case of higher dimensions $D\geq 4$ is also discussed.

math-ph↗