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Physical Review A

Reply to “Comment on ‘Conditionally exactly soluble class of potentials’ ”

ALVARO DE SOUZA DUTRA

Published May 17, 2000• 7 citations
Publisher

Abstract

We show that the problems raised by Znojil [Phys. Rev. A ▪, ▪ (2000)] preceding paper, can be resolved and that, in fact, there exist the proposed singular conditionally, exactly solvable potentials [Phys. Rev. A 47, R2435 (1993)].
DOI
10.1103/physreva.61.066102

Related papers

Comment on “Conditionally exactly soluble class of quantum potentials”

Miloslav Znojil

We detect an omission in the paper ``Conditionally exactly soluble class of quantum potentials'' by A. de Souza Dutra [Phys. Rev. A 47, R2435 (1993)]. There, two strongly singular s-wave bound-state problems have been claimed completely solvable in closed form. Unfortunately, all the displayed wave functions are merely asymptotically correct solutions which do not satisfy the appropriate threshold boundary condition. We show that the incorporation of the threshold boundary conditions only leads to a very partial exact solvability at a single energy and for special couplings.

arXiv:quant-ph/9811088•Physical Review A•May 17, 2000•53 citations

The conditionally exactly solvable potentials: A misunderstanding

Miloslav Znojil

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 $G_0=-3\\hbar/32\\mu$ and $V_2(r)=A r^{2/3}+B/r^{2/3}+g_0/r^2$ with $g_0=-5\\hbar^2/72\\mu$ has been constructed in closed form. We show that both the result and the method of its derivation are not correct.

•Nov 30, 1998•0 citations

Expanding the class of conditionally exactly solvable potentials

ALVARO DE SOUZA DUTRA, Uwe Girlich

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.

Physical Review A•Nov 1, 1994•4 citations

Reply to “Comment on ‘Solution of the Schrödinger equation for the time-dependent linear potential’ ”

I. Guedes

In this reply I discuss further the misconception in my paper [Phys. Rev. A 63, 034102 (2001)] related to the solution of the Schr\"odinger equation for a particle in a time-dependent linear potential.

Physical Review A•Jul 8, 2003•18 citations

Reply to “Comment on ‘Family of modified contracted Schrödinger equations’ ”

Diego R. Alcoba, Carmela Valdemoro

The preceding Comment by Yasuda [Phys. Rev. A 79, 016101 (2009)] on our earlier paper [Phys. Rev. A 64, 062105 (2001)] raises several objections about the modified contracted Schr\"odinger equations (MCSEs) to which we reply here. In his comment, Yasuda also questions the possibility of obtaining the exact solution of the fourth-order MCSE due to its indeterminacy. We maintain the opposite, at least from a theoretical point of view.

Physical Review A•Jan 27, 2009•2 citations

Comment on “many-body quantum system in the presence of solvable potential”

Francisco Marcelo Fernández

The European Physical Journal Plus•Apr 3, 2023•2 citations
We detect an omission in the paper ``Conditionally exactly soluble class of quantum potentials'' by A. de Souza Dutra [Phys. Rev. A 47, R2435 (1993)]. There, two strongly singular s-wave bound-state problems have been claimed completely solvable in closed form. Unfortunately, all the displayed wave functions are merely asymptotically correct solutions which do not satisfy the appropriate threshold boundary condition. We show that the incorporation of the threshold boundary conditions only leads to a very partial exact solvability at a single energy and for special couplings.
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.