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- In quantum mechanics, the state ## | \psi \rangle ## of a system that is in thermodynamic equilibrium can be expressed as a linear combination of its stationary states ## | \phi _n \rangle ## : $$ | \psi \rangle = \sum_n c_n | \phi _n \rangle $$

It permit us to express the mean value of energy as:

$$ \langle E \rangle _{\psi}= \sum_n E_n | c_n |^2 $$

- In other approach, one way to express the mean value of energy is by using the Boltzmann distribution. So my question is:

As the system is in thermodynamic equilibrium, is it allowed to think that Boltzmann distribution ## \frac{N_i}{N} = \frac{g_i e^{-\frac{E_i}{k_BT}}}{Z(T)} ## are equivalent to the ## | c_n |^2 ## ?

Thank you everybody.

Konte

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# I Stationary states -- Boltzmann distribution

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