Quasi-Exactly Solvable Spin 1/2 Schrödinger Operators

Details Quasi-Exactly Solvable Spin 1/2 Schrödinger Operators Quasi-Exactly Solvable Spin 1/2 Schrödinger Operators

1995-09-11

arxiv.org/abs/hep-th/9509057v1

J.Math.Phys. 38 (1997) 2795-2811

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, LaTeX2e using AMS-LaTeX package

Scientific paper

10.1063/1.532020

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.

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