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Power series in Physics

  1. Oct 31, 2012 #1

    CAF123

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    1. The problem statement, all variables and given/known data
    I have to show that the Planck radiation formula reduces to the Rayleigh-Jeans formula in the classical limit for blackbodies.

    3. The attempt at a solution
    I can easily show it using power series expansion of [itex] e^{(hc/\lambda kT)}[/itex] but I don't understand really why using a power series approximation makes something tend to the classical limit?

    Similarly, for [itex] E_k = mc^2(\gamma -1) [/itex] tending to [itex] \frac{mv^2}{2} [/itex], in the classical limit. The results are clear, I just don't understand why using a power series actually works.

    Many thanks.
     
  2. jcsd
  3. Oct 31, 2012 #2
    The first term (or terms) of a power series is a good approximation of a function only when its argument is small. Use any estimate of the approximation error to show that formally.

    If you can cast "classicality" as a smallness of some argument to some function, then a power series (polynomial, actually) approximation would describe the phenomenon "classically". See how that applies to these two cases.
     
  4. Oct 31, 2012 #3

    CAF123

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    What do you mean by the word 'argument' here?
     
  5. Nov 1, 2012 #4
    f(x) is function f of argument x.
     
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