Laplace—Runge—Lentz vectors for arbitrary spin and arbitrary dimension

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Nikitin, Anatoly G.^1

Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivska Str., Kyiv

01601, Ukraine^1

关键词: Arbitrary dimension;    Arbitrary spin;    Celestial mechanics;    External fields;    Hydrogen atoms;    Neutral particles;    Non-trivial;    Relativistic systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012010/pdf
DOI  :  10.1088/1742-6596/621/1/012010

来源: IOP

【 摘 要 】

Laplace-Runge-Lentz (LRL) vector is a cornerstone of celestial mechanics. It also plays an important role in quantum mechanics, being an integral of motion for the Hydrogen atom and some other systems. However, the majority of models of non-relativistic systems admitting LRL vector ignore the spin of orbital particles. In this survey a new collection of QM systems admitting LRL vector with spin is presented. It includes 2d and 3d systems with arbitrary spin, as well as systems of arbitrary dimension with spins 0, 1/2, and 1. All these systems are superintegrable and can be solved exactly. They emulate neutral particles with non-trivial multipole momenta (in particular, the neutron) interacting with a central external field.