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Does this hold in general ? (as an approximation only)

  1. Apr 12, 2007 #1


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    Does this hold in general ?? (as an approximation only)

    for every real or pure complex number 'a' can we use as an approximation:

    [tex] \sum _{n} exp(-aE_{n}) \sim \int_{-\infty}^{\infty} dx \int_{-\infty}^{\infty} dp exp(-ap^{2}-aV(x)) [/tex]

    So for every x V(x) > 0 in case of real and positive a ... then i would like to know if this approximation could be useful to describe the 'Semi-classical behaviour' of the sum over energies (trace) replaced by an integral.
  2. jcsd
  3. Apr 12, 2007 #2
    What you've written is more or less the classical partition function. It has all manner of problems at low temperatures (i.e. a goes to infinity), but as long as a is very small, this approximation works okay.
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