### Abstract

The evaluation of the average value of the position coordinate, (x), of a particle moving in a harmonic oscillator potential (V(x) = kx^{2}/2) with a small anharmonic piece (V′(x)= - λkx^{3}) 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 language | English (US) |
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Pages (from-to) | 190-194 |

Number of pages | 5 |

Journal | American Journal of Physics |

Volume | 65 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1997 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)