Generalized Master Function Approach to Quasi-Exactly Solvable Models

Details Generalized Master Function Approach to Quasi-Exactly Solvable Models Generalized Master Function Approach to Quasi-Exactly Solvable Models

2000-05-15

arxiv.org/abs/math-ph/0005016v1

Physics

Mathematical Physics

21 Pages

Scientific paper

By introducing the generalized master function of order up to four together with corresponding weight function, we have obtained all quasi-exactly solvable second order differential equations. It is shown that these differntial equations have solutions of polynomial type with factorziation properties, that is polynomial solutions Pm(E) can be factorized in terms of polynomial Pn(E) for m not equal to n. All known quasi-exactly quantum solvable models can be obtained from these differential equations, where roots of polynomial Pn(E) are corresponding eigen-values.

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