The Nonrelativistic Ground State Energy Spectra of Potential Counting Coulomb and Quad-ratic Terms in Non-commutative Two Dimensional Real Spaces and Phases (original) (raw)
Related papers
International Letters of Chemistry, Physics and Astronomy, 2015
A novel study for the exact solvability of nonrelativistic quantum spectrum systems for companied Harmonic oscillator potential and its inverse (the isotropic harmonic oscillator plus inverse quadratic potential) is discussed used both Boopp’s shift method and standard perturbation theory in both noncommutativity two dimensional real space and phase (NC-2D: RSP), furthermore the exact corrections for the spectrum of studied potential was depended on two infinitesimals parameters θ and θ¯ which plays an opposite rolls, this permits us to introduce a new fixing gauge condition and we have also found the corresponding noncommutative anisotropic Hamiltonian.
The noncommutative Coulomb potential
2021
In this work, we analyze the noncommutative three-dimensional Coulomb potential problem. For this purpose, we used the KustaanheimoStiefel mapping to write the Schrödinger equation for Coulomb potential in a solvable way. Then, the noncommutative hydrogen-like atoms were treated, and their energy levels were found. In addition, we estimate a bound for the noncommutativity parameter.
Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics
Annals of Physics, 2021
In this paper, we consider an electron moving on a 2D noncommutative plane immersed in a constant magnetic field under the influence of a polynomial potential. We obtain gauge invariant energy spectra of this system using 2-parameter family of unitarily equivalent irreducible representations of the nilpotent Lie group GNC that were worked out in detail in [7]. We work out the cases of anisotropic harmonic potential and the Hall potential as physical applications of the proposed method. We also show subsequently that straightforward generalization of the Landau problem and the quantum Hall effect in the noncommutative setting using minimal coupling prescription as is done naively on many occasions in the literature violate gauge invariance of energy spectra.
International Letters of Chemistry, Physics and Astronomy, 2017
In this work, an analytical expression for the nonrelativistic energy spectrum of some diatomic molecules was obtained through the Bopp's shift method in the noncommutative (NC) two-dimensional real space-phase symmetries (NC: 2D-RSP) with a new modified Kratzer-type potential (NMKP) in the framework of two infinitesimal parameters θ and θ due to (space-phase) noncommutativity, by means of the solution of the noncommutative Schrödinger equation. The perturbation property of the spin-orbital Hamiltonian operator and new Zeeman effect of twodimensional system are investigated. We have shown that, the new energy of diatomic molecule is the sum of ordinary energy of modified Kratzer-type potential, in commutative space, and new additive terms due to the contribution of the additive part of the NMKP. We have shown also that, the group symmetry of (NC: 2D-RSP) reduce to new subgroup symmetry of NC two-dimensional real space (NC: 2D-RSP) under new modified Kratzer-type interactions.
Noncommutative Quantum Mechanics: The Two-Dimensional Central Field
International Journal of Modern Physics A, 2002
Quantum mechanics in a noncommutative plane is considered. For a general two-dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter (θ) and explicit expressions for the eigenstates and eigenvalues are given. The Green function is explicitly obtained and we show that it can be expressed as an infinite series. For polynomial type potentials, we found a smooth limit for small values of θ and for nonpolynomial ones this limit is necessarily abrupt. The Landau problem, as a limit case of a noncommutative system, is also considered.