# Thermal populations of atomic energy eigenstates

## Main Question or Discussion Point

Basically I have an (infinite) population of isolated atoms with a bunch of discrete energy levels available to them. I want to work out what the expected population of each of the states is at a given temperature.

They're complex atoms (transition metals) and spin-orbit coupling combined with various valance configurations gives me a big spectrum of possible eigenstates, with a number of different degeneracies. I'm sure I should have covered this at some stage in my education, but I always hated statistical physics and skipped most of the lectures.

I'm hoping someone could point me towards the right formula or the right book, or even a paper that has covered this at a basic level and has useful references. The only thing I remember is looking at the fermi level in semi-conductors, but I don't think that applies when we have discrete states.

Thanks
John

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Homework Helper
The book I always liked for statistical mechanics, at least as an introduction, was "An Introduction to Thermal Physics" by Daniel Schroeder. So you might have a look at that. Basically you're going to need something like
$$P(\psi) = \frac{1}{Z}e^{(N\mu - \epsilon)/kT}$$
where $\mu$ is the chemical potential of a given state, $\epsilon$ is its energy, $N$ is the number of electrons in the state, $T$ is the temperature, and $k$ is Boltzmann's constant. I'm not sure if that's the exact notation used in the book but it should be recognizable at least.

Terrific, thankyou very much. Off to the library now.

(I reckon it's always better to have someone recommend a good book than just typing "statistical physics" in the catalogue.)