Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
نویسندگان
چکیده
We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that for a specific choice of the noncommutative parameters, the time reversal symmetry of the systems get restored since the energy spectrum becomes degenerate. This is in contrast to the noncommutative configuration space where the time reversal symmetry of the harmonic oscillator is always broken.
منابع مشابه
Super algebra and Harmonic Oscillator in Anti de Sitter space
The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...
متن کاملRepresentation of Noncommutative Phase Space
The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Schödinger equation from noncommutative space to commutative space is obtained. PACS number: 03.65Bz, 11.90.+t
متن کاملMonopole in Momentum Space in Noncommutative Quantum Mechanics
We generalize the noncommutative quantum mechanics by promoting the θ parameter to an operator which is shown to be only momentum dependent. We introduce an angular momentum satisfying the usual algebra only if the θ field has a Dirac monopole structure in momentum space. This result can be related to recent experiments in condensed matter physics. In this work, we generalize the quantum mechan...
متن کاملOn Quantum Mechanics on Noncommutative Quantum Phase Space
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ = ǫ k ij θk and a momentum noncommutativity matrix parameter βij = ǫ k ij βk, is showed to be equivalent to QuantumMechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformatio...
متن کاملThe ⋆-value Equation and Wigner Distributions in Noncommutative Heisenberg algebras∗
We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The formalism is then applied to the exactly soluble Landau and harmonic oscillator problems in the 2-dimensional noncommutative phase-space plane, in order to derive t...
متن کامل