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International Journal of Modern Physics C

Comments on two conditionally solvable quantum-mechanical models

Paolo Amore, Francisco Marcelo Fernández

Published Oct 6, 2021• 2 citations
Publisher

Abstract

We analyze the results published in this journal about two conditionally solvable quantum-mechanical models. We show that the authors failed to derive the spectrum correctly because they did not take into consideration all the roots of the truncation condition used for that aim and did not interpret them correctly.
DOI
10.1142/s012918312250036x

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In the paper "Conditionally exactly soluble class of quantum potentials" by A. de Souza Dutra [Phys. Rev. A 47 (1993) R2435] the whole s−s-s−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^2V1​(r)=A/r+B/r1/2+G0​/r2 with G0=−3hbar/32muG_0=-3\\hbar/32\\muG0​=−3hbar/32mu and V2(r)=Ar2/3+B/r2/3+g0/r2V_2(r)=A r^{2/3}+B/r^{2/3}+g_0/r^2V2​(r)=Ar2/3+B/r2/3+g0​/r2 with g0=−5hbar2/72mug_0=-5\\hbar^2/72\\mug0​=−5hbar2/72mu has been constructed in closed form. We show that both the result and the method of its derivation are not correct.