A probability-conserving dissipative Schr\"odinger equation

Dissipative effects on a microscopic level are included in the Schr\"odinger equation. When the decay between different local levels as a result of the coupling to a bath, the Schr\"odinger equation no longer conserves energy, but the probability of the states is conserved. The procedure is illustrated with several examples that include direct electronic decay and damping of local phonons (vibrational levels). This method significantly reduces the calculational effort compared to conventional density matrix techniques.