# Bose Equilibrium Distribution and Atomic Units

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1. Feb 2, 2016

### Raptor112

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. Feb 2, 2016

### 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
3. Feb 2, 2016

### Raptor112

According to wikipedia it's just one by definition:

https://en.wikipedia.org/wiki/Boltzmann_constant

4. Feb 2, 2016