Schr”dinger Equations and Diffusion Theory addresses the question "What is the Schr”dinger equation?" in terms of diffusion processes, and shows that the Schr”dinger equation and diffusion equations in duality are equivalent. In turn, Schr”dinger's conjecture of 1931 is solved. The theory of diffusion processes for the Schr”dinger equation tell us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles.
The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schr”dinger equations.
The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schr”dinger equation, namely, quantum mechanics.
The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.
Introduction and motivation; diffusion processes and their transformations; duality and time reversal of diffusion processes; equivalence of diffusion and Schroedinger equations; variational principle; diffusion processes in q-representation; segregation of a population; the Schroedinger equation can be a Boltzmann equation; applications of the statistical model for Schroedinger equations; relative entropy and Csiszar's projection; large deviations; non-linearity induced by the branching property.
Series: Monographs in Mathematics
Number Of Pages: 340
Published: 1st July 1993
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.4 x 15.6
Weight (kg): 0.64