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Expand and derive the planck occupanncy

  1. May 4, 2013 #1
    1. The problem statement, all variables and given/known data
    The average energy of a harmonic oscillator is written using Boltzman statistics as:

    <ε> = (<n> +.5) = [itex]\frac{\sum_{n} ε_{n} exp \frac{-ε_{n}}{kt}}{\sum_{n} exp \frac{-ε_{n}}{kt}}[/itex]

    Expand the expontentials and hence derive the Planck Occupancy
    <n> = n(ω,T) =[itex]\frac{1}{exp\frac{h bar * ω}{kT}-1}[/itex]

    2. Relevant equations
    The two are above in part 1


    3. The attempt at a solution
    I have not been able to even start this question as I cannot understand what is meant by the expand the exponentials. Any help to start this off would be greatfull and as I have been stuck on this for nearly an hour.
    Thank you
     
  2. jcsd
  3. May 4, 2013 #2
    Basically, it is asking you to evaluate the sums.
     
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