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

Quantum Physics 2009-10-31 v2

Abstract

In the paper "Conditionally exactly soluble class of quantum potentials" by A. de Souza Dutra [Phys. Rev. A 47 (1993) R2435] the whole ss-wave spectrum of bound states in potentials V1(r)=A/r+B/r1/2+G0/r2V_1(r)=A/r+B/r^{1/2}+G_0/r^2 with G0=3/32μG_0=-3\hbar/32\mu and V2(r)=Ar2/3+B/r2/3+g0/r2V_2(r)=A r^{2/3}+B/r^{2/3}+g_0/r^2 with g0=52/72μg_0=-5\hbar^2/72\mu has been constructed in closed form. We show that both the result and the method of its derivation are not correct.

Cite

@article{arxiv.quant-ph/9811088,
  title  = {The conditionally exactly solvable potentials: A misunderstanding (comment on "Conditionally exactly soluble class of quantum potentials")},
  author = {Miloslav Znojil},
  journal= {arXiv preprint arXiv:quant-ph/9811088},
  year   = {2009}
}

Comments

extended and published version

R2 v1 2026-07-22T20:05:06.978Z