Eigenvalue problem of the Liouville-von Noumann operater for quantum scattering process is extended to a class of eigenstates (density matrices) which have the delta function singularity in the momentum representation. The eigenstates are, therefore, entirely decolarized in space. This corresponds to a situation where the S-matrix theory is not applicable. The solution of the eigenvalue equation leads to a new irreducible representation of denstity matrix where eigenstates of the Liouville-von Noumann operater cannot be reduced to products of wave functions. These eigenstates have complex eigenvalues; i.e., they have a broken time symmetry. Only a possible eigenstate with zero eigenvalue is maicrocanonical state. This zero eigenvalue is isolated from other non-vanishing complex eigenvalues. Hence, we have approach to microcanonical equilibrium. By the irreducible representation the Pauli master equation is derived from dynamics without any statistical operations.