Quasi-Exactly Solvable Spin 1/2 Schr\"odinger Operators
Federico Finkel, Artemio Gonzalez-Lopez, Miguel A. Rodriguez (Dept. of, Theoretical Physics II, Universidad Complutense, Madrid)
TL;DR
This paper investigates the algebraic structures that enable quasi-exact solvability of one-dimensional spin 1/2 Schrödinger operators, providing conditions for their characterization and constructing new examples.
Contribution
It establishes necessary and sufficient conditions for matrix differential operators to be equivalent to Schrödinger operators and introduces new multi-parameter QES spin 1/2 Hamiltonians.
Findings
Derived conditions for QES operators
Simplified the characterization process
Constructed new multi-parameter QES Hamiltonians
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.
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