Lewis-Riesenfeld approach to the solutions of the Schrödinger equation in the presence of a time-dependent linear potential

Pi Gang Luan, Chi Shung Tang

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

We reexamine the general solution of a Schrödinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space and then Fourier transform the solution to get the general wave function. Appropriately choosing the weight function in the latter method, we can obtain the same wave function as the former method. It is found that a non-Hermitian time-dependent linear invariant can be used to obtain Gaussian-type wave-packet solutions of the time-dependent system. This operator is a specific linear combination of the initial momentum and initial position operators. This fact indicates that the constants of integration such as the initial position and initial momentum that determine the classical motion play important roles in the time-dependent quantum system. The eigenfunction of the linear invariant is interpreted as a wave packet with a "center of mass" moving along the classical trajectory, while the ratio between the coefficients of the initial position and initial momentum determines the width of the wave packet.

Original languageEnglish
Article number014101
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume71
Issue number1
DOIs
StatePublished - 1 Jan 2005

Fingerprint

Dive into the research topics of 'Lewis-Riesenfeld approach to the solutions of the Schrödinger equation in the presence of a time-dependent linear potential'. Together they form a unique fingerprint.

Cite this