Nonrelativistic quantum mechanics as a noncommutative Markof process

S. Chaturvedi, R. Jagannathan, V. Srinivasan +1 more

H. O. Girotti

We discuss the main features of noncommutative quantum mechanics, a version of nonrelativistic quantum mechanics that involves noncommuting coordinates. After finding a representation for the algebra obeyed by the coordinates and momenta, we analyze the changes due to the noncommutative nature of the coordinates. The noncommutative two-dimensional harmonic oscillator is discussed in detail. Under certain restrictions, the effect of the noncommutativity is found to be equivalent to a Landau interaction. The modifications produced by the noncommutativity on the thermodynamic functions of the oscillator also are studied.

Halqem, Nizamidin, Abduwali +5 more

我们学习一个中立粒子的 noncommutative nonrelativistic 量动力学，它拥有一电的 qaudrupole 时刻，面对一个外部磁场。由为磁场介绍移动，首先，我们给 Schr ? dinger 方程两个都分别地在一个 noncommutative 空格和 noncommutative 面对一个外部磁场分阶段执行空间。然后由解决 Schr ? dinger 方程两个都在一个 noncommutative 空格和 noncommutative 分阶段执行空间，我们分别地获得电的四极时刻的量阶段。我们证明这些阶段是几何、散的。

Eduard Prugovečki

Vladimir Dmitriev

Abdelmadjid Maireche

In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, the deformed Klein–Gordon and Schrödinger equations were solved with the modified equal vector scalar Manning-Rosen potential that has been of significance interest in recent years using Bopp's shift method and standard perturbation theory in the first-order in the noncommutativity parameters in 3-dimensions noncommutative quantum mechanics. By employing the improved approximation of the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, and Ar2). The obtained energy eigenvalues appear as a function of the generalized Gamma function, the parameters of noncommutativity, and the parameters of studied potential, in addition to the atomic quantum numbers . In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result is consistent with what is obtained in the literature. We have seen that the improved approximation of the centrifugal term is better than the other approximations in finding the approximate analytical solutions of the Klein-Gordon and Schrödinger equations for the modified Manning–Rosen potential in RNCQM and NRNCQM.