quantum statistical treatment

Expansion in Fock state

A general expansion of $\rho$

$$ \rho=\sum C_{nm}| n\rang\lang m| $$

the reduced expansion

$$ \rho =\sum P_n|n\rang\lang n| $$

Expansin in Coherent state

$$ \rho =\int_{\mathbb C}P(\alpha)|\alpha\rang\lang\alpha|d^2\alpha. $$