Remarks on connections between quantum mechanics and stochastic quantizaion

道夫 西岡

Sheldon Goldstein

Bhashyam Balaji

The mathematical similarities between quantum mechanics and stochastic processes has been studied in the literature. Some of the major results are reviewed, such as the relationship between the Fokker-Planck equation and the Schrödinger equation. Also reviewed are more recent results that show the mathematical similarities between quantum many particle systems and concepts in other areas of applied science, such as stochastic Petri nets. Some connections to filtering theory are discussed.

’J. Ogunlana

Sergio A Albeverio, Raphael J. Høegh-Krohn

We prove that the solution of Nelson's stochastic mechanics equation associated with any stationary solution ψ of the Schrödinger equation is the homogeneous Markov process of the heat equation with Dirichlet boundary condition on the hypersurface ψ=0.

Giovanni Jona-Lasinio