Integrable and superintegrable systems with spin in three-dimensional Euclidean space
Mathematical Physics
2012-10-11 v2 math.MP
Abstract
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components of linear momentum. Several such systems are found and for one non-trivial example we show how superintegrability leads to exact solvability: we obtain exact (nonperturbative) bound state energy formulas and exact expressions for the wave functions in terms of products of Laguerre and Jacobi polynomials.
Cite
@article{arxiv.0906.1021,
title = {Integrable and superintegrable systems with spin in three-dimensional Euclidean space},
author = {P. Winternitz and I. Yurdusen},
journal= {arXiv preprint arXiv:0906.1021},
year = {2012}
}
Comments
23 pages