Quasi-Exactly Solvable Spin 1/2 Schrödinger Operators

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.

32 pages, LaTeX2e using AMS-LaTeX package

References in corpus (3)

• Quasi Exactly Solvable 2$\times$2 Matrix Equations
• Real Lie Algebras of Differential Operators and Quasi-Exactly Solvable Potentials
• Central potential and examples of hidden algebra structure

Cited by in corpus (6)

• Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems
• Quasi Exactly Solvable NxN-Matrix Schroedinger Operators
• Quasi exactly solvable matrix models in sl(n)
• Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold
• QES systems, invariant spaces and polynomials recursions
• Quasi exactly solvable matrix Schroedinger operators