  The derivation of the time dependent Schr\"odinger equation with transversal
and longitudinal relaxation, as the quantum mechanical analog of the classical
Landau-Lifshitz-Bloch equation, has been described. Starting from the classical
Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been
performed and the corresponding von-Neumann equation deduced. In a second step
the time Schr\"odinger equation has been derived. Analytical proofs and
computer simulations show the correctness and applicability of the derived
Schr\"odinger equation.
