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Finkel, Federico; González-López, Artemio; Rodríguez, Miguel A.

Quasi-exactly solvable \(\text{spin}1/2\) Schrödinger operators. (English) Zbl 0877.35031

J. Math. Phys. 38, No. 6, 2795-2811 (1997).
Summary: The algebraic structures underlying quasi-exact solvability for spin l/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 Schrödinger operator are found. Systematic simplifications of these conditions are analyzed, and are then applied to the construction of new examples of multi-parameter QES spin 1/2 Hamiltonians in one dimension.

Cited in 4 Documents

MSC:

35J10 Schrödinger operator, Schrödinger equation
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Keywords:

multi-parameter Hamiltonians; quasi-exact solvability
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References:

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