  This paper is concerned with the connection between density matrix method,
supersymmetric quantum mechanics and Lewis-Riesenfeld invariant theory. It is
shown that these three formulations share the common mathematical structure:
specifically, all of them have the invariant operators which satisfies the
Liouville-Von Neumann equation and the solutions to the time-dependent
Schr\"{o}dinger equation and/or Schr\"{o}dinger eigenvalue equation can be
constructed in terms of the eigenstates of the invariants.
