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Somebody asked me the following. Anybody want to give it a go?

"Consider the following.

We know, from elementary quantum mechanics, that the Bohr energies

of the hydrogen atom go as (-E_0 / n^2), where n is, of course, the

principal quantum number.

We also know, from elementary statistical mechanics, that the

partition function of a system is the sum of exp (-E / k T), over all states.

Taken together, one can easily demonstrate that the partition

function of the hydrogen atom actually diverges.

How can this be? What is the resolution to this apparent paradox?"