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General solution of a system of differential equations modelling a class of exactly-solvable potentials. II: Extended results. (English) Zbl 1033.81029

Author’s abstract: The complete, closed-form solution of a system of coupled equations introduced by M.-L. Ge et al. [Phys. Rev. A (3) 62, 052110, 7 pp. (2000)] and representing a set of potentials for which shift operators can be constructed is given. The general solution obtained can be used to perform a systematic search for new exactly-solvable potentials. This note is an extension of Part I in Proc. Est. Acad. Sci., Phys. Math. 50, 42–48 (2001; Zbl 1139.81392).

MSC:

81U15 Exactly and quasi-solvable systems arising in quantum theory
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
47E05 General theory of ordinary differential operators
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

Citations:

Zbl 1139.81392
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