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Physical Review A

Reply to “Comment on Exact wave function of a harmonic plus an inverse harmonic potential with time-dependent mass and frequency”

Chung‐In Um, Shang-Moon Shin, Kyu-Hwang Yeon, Thomas F. George

Published Jan 13, 2000• 7 citations
Publisher

Abstract

In reply to the Comment by Maamache on Phys. Rev. A 58, 1574 (1998), it is shown first that the $\mathrm{M\ifmmode\ddot\else\textasciidieresis\fi{}}(t)$ terms are canceled and then that the wave function [Eq. (34)] is an eigenfunction of the invariant of Eq. (19).

DOI
10.1103/physreva.61.026103

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Comment on “Exact wave function of a harmonic plus an inverse harmonic potential with time-dependent mass and frequency”

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Comment on “Wave functions of a time-dependent harmonic oscillator in a static magnetic field”

Mustapha Maamache, Abdelhafid Bounames, N. Ferkous

We show that the procedure used by Ferreira et al. [Phys. Rev. A 66, 024103 (2002)] is not correct for the following reasons: (i) the invariant $I(t)$ they derived does not satisfy the Liouville--Von Neuman equation. (ii) They found that the eigenvalues of $I(t)$ are time dependent which should not be the case according to the Lewis-Riesenfeld theory. We give a correct procedure to find the solution of the system they considered, i.e., the Schr\"odinger equation for a two-dimensional harmonic oscillator with time-dependent mass and frequency in the presence of a static magnetic field.

Physical Review A•Jan 24, 2006•17 citations
In reply to the Comment by Maamache on Phys. Rev. A 58, 1574 (1998), it is shown first that the M\ifmmode\else¨\textasciidieresis\fi(t)\mathrm{M\ifmmode\ddot\else\textasciidieresis\fi{}}(t)M\ifmmode\else¨​\textasciidieresis\fi(t) terms are canceled and then that the wave function [Eq. (34)] is an eigenfunction of the invariant of Eq. (19).
We show that the procedure used by Ferreira et al. [Phys. Rev. A 66, 024103 (2002)] is not correct for the following reasons: (i) the invariant I(t)I(t)I(t) they derived does not satisfy the Liouville--Von Neuman equation. (ii) They found that the eigenvalues of I(t)I(t)I(t) are time dependent which should not be the case according to the Lewis-Riesenfeld theory. We give a correct procedure to find the solution of the system they considered, i.e., the Schr\"odinger equation for a two-dimensional harmonic oscillator with time-dependent mass and frequency in the presence of a static magnetic field.