Bose Equilibrium Distribution and Atomic Units

[Raptor112]

Homework Statement

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?

Homework 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?

 

[DrClaude]

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.

 

[Raptor112]

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.

According to wikipedia it's just one by definition:

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

 

[DrClaude]

According to wikipedia it's just one by definition:

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

Right, I was wrong. T will not be expressed in kelvins, see https://en.wikipedia.org/wiki/Natural_units#Atomic_units