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New class of conditionally exactly solvable potentials in quantum mechanics. (English) Zbl 0851.34080

Summary: Motivated by an idea of Dutra, we obtain a new class of one-dimensional conditionally exactly solvable potentials for which the entire spectra can be obtained in an algebraic manner provided one of the potential parameters is assigned a fixed negative value. It is shown that using shape-invariant potentials as input, one may generate different classes of such potentials even in more than one dimension. We also illustrate that WKB and supersymmetry inspired WKB methods provide very good approximations for these potentials with the latter doing comparatively better.

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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