Quantum Mechanics as a Generalized Stochastic Theory in Phase Space.
Abstract
A class of multitime phase space distribution functions are presented such that an arbitrary quantum multitime correlation function can be expressed as a phase space average of the form encountered in classical stochastic theories. The nonclassical features of these multitime distribution functions are studied and it is shown that they may be considered as characterizing a generalized stochastic process in phase space. It is demonstrated that the multitime distribution functions that correspond to Hamiltonian evolution of isolated quantum systems, satisfy a certain condition that may be regarded as characterizing a generalized Markov process. Also investigated are certain special features of the generalized stochastic processes that characterize the evolution of open systems. Finally, the relation between the formulation presented and some previous attempts to formulate quantum mechanics as a Markov process in phase space is discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 February 1976
 Bibcode:
 1976PhDT........60S
 Keywords:

 Physics: General;
 PhaseSpace Integral;
 Quantum Mechanics;
 Stochastic Processes;
 Distribution Functions;
 Hamiltonian Functions;
 Markov Processes;
 Momentum;
 Position (Location);
 Thermodynamics and Statistical Physics