White Noise Calculus and Hamiltonian of a Quantum Stochastic Process

Abstract

A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick's and Ito's theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and the conditions for unitarity have been proven. The Hamiltonian of the associated one parameter strongly continuous group has been calculated explicitely.