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Physical Review A

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

I. Guedes

Published Jul 8, 2003• 18 citations
Publisher

Abstract

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.
DOI
10.1103/physreva.68.016102

Related papers

Comment on “Solution of the Schrödinger equation for the time-dependent linear potential”

Hacene Bekkar, Farid Benamira, Mustapha Maamache

We present the correct way to obtain the general solution of the Schr\"odinger equation for a particle in a time-dependent linear potential following the approach used in the paper of Guedes [Phys. Rev. A 63, 034102 (2001)]. In addition, we show that, in this case, the solutions (wave packets) are described by the Airy functions.

Physical Review A•Jul 8, 2003•44 citations

Comment on “Solution of the Schrödinger equation for the time-dependent linear potential”

Jarosław H. Bauer

It is shown that the wave function recently found by Guedes [Phys. Rev. A 63, 034102 (2001)] is a special case of the well-known Volkov solution to the time-dependent Schr\"odinger equation describing a nonrelativistic charged particle moving in an electromagnetic field.

Physical Review A•Mar 1, 2002•33 citations

Comment on "Solutions of the Schrödinger equation for the time-dependent linear potential''

Jian Qi Shen

We show that the solution obtained by Bekkar {\it et al.} in their comment [Phys. Rev. A {\bf 68}, 016101 (2003)] on Guedes's work of solving the quantum system with a time-dependent linear potential is still {\it not} the {\it general} one of the Schrödinger equation. It is concluded that Bekkar {\it et al.}'s solution (corresponding to the linear Lewis-Riesenfeld invariant) and our solution (corresponding to the quadratic-form Lewis-Riesenfeld invariant) presented here will constitute together a complete set of solutions (general solutions) of the time-dependent Schrödinger equation of the system under consideration.

arXiv:quant-ph/0311002•Nov 1, 2003•0 citations

On the time‐dependent solutions of the Schrödinger equation. I. The linear time‐dependent potential

A. Palma, M. Villa, L. Sandoval

Abstract The solution of the Schrödinger equation for the linear time‐dependent potential has recently been the subject of several publications. In this report, we show this is one of the few systems that leads to a solvable Lie algebra. In fact, we consider a more general problem where the linear time‐dependent potential is only a particular case. The solution is found by using the well‐known theorem of Wei‐Norman. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

International Journal of Quantum Chemistry•Jul 8, 2010•7 citations

Solution of the Schrödinger equation for the time-dependent linear potential

I. Guedes

In this paper I have drawn out the steps to be followed in order to derive the exact Schr\"odinger wave function for a particle in a general one-dimensional time-dependent linear potential. To this end I have used the so-called Lewis and Riesenfeld invariant method, which is based on finding an exact quantum-mechanical invariant in whose eigenstates the exact quantum states are found. In particular, I have obtained the wave functions of a particle in the linear potential well, driven by a monochromatic electric field.

Physical Review A•Feb 12, 2001•90 citations

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 +1 more

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).

Physical Review A•Jan 13, 2000•7 citations
We show that the solution obtained by Bekkar {\it et al.} in their comment [Phys. Rev. A {\bf 68}, 016101 (2003)] on Guedes's work of solving the quantum system with a time-dependent linear potential is still {\it not} the {\it general} one of the Schrödinger equation. It is concluded that Bekkar {\it et al.}'s solution (corresponding to the linear Lewis-Riesenfeld invariant) and our solution (corresponding to the quadratic-form Lewis-Riesenfeld invariant) presented here will constitute together a complete set of solutions (general solutions) of the time-dependent Schrödinger equation of the system under consideration.
In this paper I have drawn out the steps to be followed in order to derive the exact Schr\"odinger wave function for a particle in a general one-dimensional time-dependent linear potential. To this end I have used the so-called Lewis and Riesenfeld invariant method, which is based on finding an exact quantum-mechanical invariant in whose eigenstates the exact quantum states are found. In particular, I have obtained the wave functions of a particle in the linear potential well, driven by a monochromatic electric field.