Evolution of the Quantum States of a Harmonic Oscillator in a Uniform Time Varying Electric Field
作者:
G. W. Parker,
期刊:
American Journal of Physics
(AIP Available online 1972)
卷期:
Volume 40,
issue 1
页码: 120-125
ISSN:0002-9505
年代: 1972
DOI:10.1119/1.1986457
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
When a system of particles in a bound state is placed in an external field the quantum state of the system depends on the manner in which the field is produced. The two limiting cases of interest are the adiabatic and impulse limits. Since the system does not approach a stationary state in either limit, in general, it is necessary to consider solutions of the time dependent Schrödinger equation. An example of this approach is provided by the problem of a harmonic oscillator in a uniform, time varying electric field for which an exact solution is easy to obtain using the Magnus expansion for the evolution operator. This operator contains the position and momentum in a particularly simple way that allows it to be interpreted in terms of position and momentum shifts produced by the field. The wavefunction of the oscillator is obtained in the adiabatic and impulse limits assuming the field to be switched on in an exponential fashion. Results obtained for these two limiting cases are then shown to be independent of the manner in which the field reaches its final steady value.
点击下载:
PDF
(546KB)
返 回