Geometry of the Time-Dependent Variational Principle in Quantum Mechanics

Abstract

In the present paper we study the geometry of the time-dependent variational principle in quantum mechanics. This principle which we abbreviate as TDVP is a formulation of the time-dependent Schrödinger equation is obtained by requiring tht the action functional be stationary under free variation of the time-dependent state. Many applications of this principle are obtained by introducing a finite set of parameters and performing a restriced variation with respect to the time dependence of these parameters.