Some remarks about the time-dependent Schrödinger equation with damping

Abstract

Abstract The missing derivation of the time-dependent Schrödinger equation following Schrödinger’s original description of the time-independent Schrödinger equation. Also, this description is extended to derive the Caldirola-Kanai, the Schuch-Schrödinger, and the Gisin-Schrödinger equation. In the second part, the Gisin-Schrödinger equation will be derived once more using the Ito formalism of stochastic differential equations. Furthermore, we discuss the extension to larger spin-system using the cluster mean-field theory.