Abstract
Expansion formulas for density matrices are derived with the use of the calculus of ordered exponentials. Using the formulas the expressions for virial coefficients are explicitly obtained. The expression of the third virial coefficient is calculated to obtain its expansion formula in terms of \(\hbar^{2}\beta/M\). The expansion formulas for density matrices can be used to derive a new formula of multiple scattering, which involves Luttinger and Kohn's formula as a special case. The expansion formula for the normalized density matrix is also given. Expansion formulas which are to the applied to irreversible processes and relaxation phenomena are also given.
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