dorsal/arxiv
View SchemaLewis-Riesenfeld approach to the solutions of Schrodinger equation in the presence of the presence of a time-dependent linear potential
| Authors | Pi-Gang Luan, Chi-Shung Tang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309174 |
| URL | https://arxiv.org/abs/quant-ph/0309174 |
| DOI | 10.1103/PhysRevA.71.014101 |
| Journal | Physical Review A 71, 014101 (2005) |
Abstract
We reexamine the general solution of a Schr\"{o}dinger 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 non-Hermitian time-dependent linear invariant can be used to obtain Gaussian-type wave-packet (GTWP) 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.
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"abstract": "We reexamine the general solution of a Schr\\\"{o}dinger equation in the\npresence of a time-dependent linear potential in configuration space based on\nthe Lewis-Riesenfeld framework. For comparison, we also solve the problem in\nmomentum space and then Fourier transform the solution to get the general wave\nfunction. Appropriately choosing the weight function in the latter method, we\ncan obtain the same wave function as the former method. It is found that\nnon-Hermitian time-dependent linear invariant can be used to obtain\nGaussian-type wave-packet (GTWP) solutions of the time-dependent system. This\noperator is a specific linear combination of the initial momentum and initial\nposition operators. This fact indicates that the constants of integration such\nas the initial position and initial momentum that determine the classical\nmotion play important roles in the time-dependent quantum system. The\neigenfunction of the linear invariant is interpreted as a wave packet with a\n\"center of mass\" moving along the classical trajectory, while the ratio between\nthe coefficients of the initial position and initial momentum determines the\nwidth of the wave packet.",
"arxiv_id": "quant-ph/0309174",
"authors": [
"Pi-Gang Luan",
"Chi-Shung Tang"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.71.014101",
"journal_ref": "Physical Review A 71, 014101 (2005)",
"title": "Lewis-Riesenfeld approach to the solutions of Schrodinger equation in the presence of the presence of a time-dependent linear potential",
"url": "https://arxiv.org/abs/quant-ph/0309174"
},
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