Non-Commutative Quantum Mechanics
By J. Gamboa, M. Loewe, J. C. Rojas. 2000
286 citations recorded by the source corpus.
A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $\theta $, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction $V(r)$ is replaced by $V = V ({\hat H}_{HO}, {\hat L}_z)$, where ${\hat H}_{HO}$ is the hamiltonian of the two-dimensional harmonic oscillator and ${\hat L}_z$ is z- component of the angular momentum. For other finite values of $\theta$ the model can be solved by using perturbation theory.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6b363f5f74156fc2810f56492d6c62bd77d52a91
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In Statistical and Nonlinear Physics
Citations in the corpus
- THE LANDAU PROBLEM AND NONCOMMUTATIVE QUANTUM MECHANICS (2001, methodology): “ in the Schr¨odinger equation in a noncommutative plane V(x)⋆ψ(x) = V(x− 1 2 p˜)ψ(x), (3) where ⋆denotes the Moyal product and ˜p i k = θikjkp jk θ ij = θǫ ij. Then for a two dimensional central field [4] V(|x|2), (3) yields V(|x|2)⋆ψ(x) = V(ˆℵ)ψ(x), (4) where the aleph (ℵ) operator is defined as ℵˆ =”