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Ideal gas in potential step

See attached file.

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There was a mistake in the problem:

Z_{g} = Sum over N of Z(N) Exp(beta mu N)

and NOT:

Z_{g} = Sum over N of Z(N) Exp(- mu N)
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begin{document}
title{Partition function}
date{}
author{}
maketitle
I'll denote ...

Solution Summary

A detailed solution is given.

$2.19