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I'm stuck on "the summit of statistical mechanics" (as Feynman calls it): the definition of the Boltzmann Factor.

The probability of measuring the system with energy E is P(E) = 1/Z * e^-E/kT.

I've taken courses in QM and can't understand why P(E) does not depend on the ket of the system |psi>.

From QM, I want to write down P(Ei) = <psi|Ei><Ei|psi>. So why doesn't 1/Z * e^-E/kT depend on |psi>? Is it a hidden assumption about the nature of the system that all |psi> in the Hilbert Space have P(Ei) equal?

Thanks in advance,

Andrew