Average value of position for the anharmonic oscillator

Classical versus quantum results

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)190-194
Number of pages5
JournalAmerican Journal of Physics
Volume65
Issue number3
DOIs
StatePublished - Jan 1 1997

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oscillators
statistical mechanics
ladders
harmonic oscillators
quantum mechanics
thermal expansion
perturbation theory
formalism
operators
expansion
evaluation

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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Average value of position for the anharmonic oscillator : Classical versus quantum results. / Robinett, Richard Wallace.

In: American Journal of Physics, Vol. 65, No. 3, 01.01.1997, p. 190-194.

Research output: Contribution to journalArticle

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