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Paper   IPM / Physic / 6780
School of Physics
  Title:   Generalized Master Function Approach to One-Dimensional Quasiexactly Solvable Models
1.  M.A. Jafarizadeh
2.  S.J. Akhtarshenas
  Status:   Published
  Journal: J. Math. Phys.
  No.:  27
  Vol.:  41
  Year:  2000
  Pages:   7783-7796
  Supported by:  IPM
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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