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The conditionally exactly solvable potentials: A misunderstanding (comment on "Conditionally exactly soluble class of quantum potentials")

Miloslav Znojil
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Abstract

In the paper "Conditionally exactly soluble class of quantum potentials" by A. de Souza Dutra [Phys. Rev. A 47 (1993) R2435] the whole $s-$wave spectrum of bound states in potentials $V_1(r)=A/r+B/r^{1/2}+G_0/r^2$ with $G_0=-3\hbar/32μ$ and $V_2(r)=A r^{2/3}+B/r^{2/3}+g_0/r^2$ with $g_0=-5\hbar^2/72μ$ has been constructed in closed form. We show that both the result and the method of its derivation are not correct.

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Miloslav Znojil. 2003-02-10. The conditionally exactly solvable potentials: A misunderstanding (comment on "Conditionally exactly soluble class of quantum potentials"). https://doi.org/10.1103/physreva.61.066101

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