Abstract
In their recent note [J. Math. Chem. 16 (1994) 211-215], Simsek and Yalçin claim the elementary exact solvability of an s-wave radial Schrödinger equation with a shifted Pöschl-Teller potential. We re-derive and correct their formulae and weaken their conclusions: Their Jacobi polynomial wavefunctions do not comply with a boundary condition in the origin. After its inclusion, at most a triplet of their quasi-exact bound states may survive, and we have to return to non-polynomial hypergeometric wavefunctionsψ0(r) in general.
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Znojil, M. Jacobi polynomials and bound states. J Math Chem 19, 205–213 (1996). https://doi.org/10.1007/BF01165184
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DOI: https://doi.org/10.1007/BF01165184