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Physical Review A

Expanding the class of conditionally exactly solvable potentials

ALVARO DE SOUZA DUTRA, Uwe Girlich

Published Nov 1, 1994• 4 citations
Publisher

Abstract

Recently a class of quantum-mechanical potentials was presented that is characterized by the fact that they are exactly solvable only when some of their parameters are fixed to a convenient value, so they were christened as conditionally exactly solvable potentials. Here we intend to expand this class by introducing examples in two dimensions. As a byproduct of our search, we found also another exactly solvable potential.

DOI
10.1103/physreva.50.4369

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Recently a class of quantum-mechanical potentials was presented that is characterized by the fact that they are exactly solvable only when some of their parameters are fixed to a convenient value, so they were christened as conditionally exactly solvable potentials. Here we intend to expand this class by introducing examples in two dimensions. As a byproduct of our search, we found also another exactly solvable potential.
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.