1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Bose Equilibrium Distribution and Atomic Units

  1. Feb 2, 2016 #1
    1. The problem statement, all variables and given/known data
    For my project I need to compute the average the number of photons given by the expression:
    ##\bar{n}= \frac{e^{-\bar{h}\omega/\kappa T}}{1-e^{-\bar{h} \omega / \kappa T}}##
    where ##\kappa## is the Boltzmann constant and ##\omega## is the oscillator frequency. For the Hamiltonian in my project simulation, ##\bar{h} =1## so how would ##\bar{n}## be expressed?
    2. Relevant equations
    Is it as simple as ##\bar{h} =1## in the expression of ##\bar{n}## so:

    ##\bar{n}= \frac{e^{-\omega/\kappa T}}{1-e^{\omega / \kappa T}}##

    but then doesn't the argument of the exponential has dimensions, as opposed to being dimensionless which is what it's supposed to be?
     
  2. jcsd
  3. Feb 2, 2016 #2

    DrClaude

    User Avatar

    Staff: Mentor

    You have to express all quantities in atomic units. For instance, ω will be in units of the inverse of the atomic unit of time. There is no atomic unit of temperature, so T will still be in kelvin, but you have to calculate the correct value for the Boltzmann constant.
     
    Last edited: Feb 2, 2016
  4. Feb 2, 2016 #3
    According to wikipedia it's just one by definition:

    https://en.wikipedia.org/wiki/Boltzmann_constant
     
  5. Feb 2, 2016 #4

    DrClaude

    User Avatar

    Staff: Mentor

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted