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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.

 

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