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Hermitian quasi-exactly solvable matrix Shroedinger operators

Stanislav Spichak·Renat Zhdanov
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Abstract

We construct six multi-parameter families of Hermitian quasi-exactly solvable matrix Schroedinger operators in one variable. The method for finding these operators relies heavily upon a special representation of the Lie algebra o(2,2) whose representation space contains an invariant finite-dimensional subspace. Besides that we give several examples of quasi-exactly solvable matrix models that have square-integrable eigenfunctions. These examples are in direct analogy with the quasi-exactly solvable scalar Schroedinger operators obtained by Turbiner and Ushveridze.

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Stanislav Spichak, Renat Zhdanov. 1998-12-01. Hermitian quasi-exactly solvable matrix Shroedinger operators. https://arxiv.org/abs/math-ph/9812001

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