Average value of position for the anharmonic oscillator: Classical versus quantum results
作者:
Richard W. Robinett,
期刊:
American Journal of Physics
(AIP Available online 1997)
卷期:
Volume 65,
issue 3
页码: 190-194
ISSN:0002-9505
年代: 1997
DOI:10.1119/1.18747
出版商: American Association of Physics Teachers
关键词: 03.65;05.20
数据来源: AIP
摘要:
The evaluation of the average value of the position coordinate,〈x〉, of a particle moving in a harmonic oscillator potential(V(x)=kx2/2)with a small anharmonic piece(V(x)=−λkx3)is a standard calculation in classical Newtonian mechanics and statistical mechanics where the problem has relevance to thermal expansion. In each case, the calculation is most easily done using a perturbative expansion. In this note, we perform the same computation of〈x〉in quantum mechanics using time-independent perturbation theory and the ladder operator formalism to show how similar results are obtained. We also indicate how a semiclassical calculation using a classical probability distribution can also be used to obtain the same result.
点击下载:
PDF
(157KB)
返 回