Quasi-Exactly Solvable Spin 1/2 Schr\"odinger Operators
High Energy Physics - Theory
2009-10-28 v1
Abstract
The algebraic structures underlying quasi-exact solvability for spin 1/2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order differential operator preserving a space of wave functions with polynomial components to be equivalent to a \sch\ operator are found. Systematic simplifications of these conditions are analyzed, and are then applied to the construction of several new examples of multi-parameter QES spin 1/2 Hamiltonians in one dimension.
Keywords
Cite
@article{arxiv.hep-th/9509057,
title = {Quasi-Exactly Solvable Spin 1/2 Schr\"odinger Operators},
author = {Federico Finkel and Artemio Gonzalez-Lopez and Miguel A. Rodriguez},
journal= {arXiv preprint arXiv:hep-th/9509057},
year = {2009}
}
Comments
32 pages, LaTeX2e using AMS-LaTeX package