Langevin formulation of quantum mechanics

L. S. F. Olavo, Luciano C. Lapas, A. Figueiredo

Bernadette Bensaude‐Vincent, Francis A Duck

N. G. van Kampen, Irwin Oppenheim

H Okamoto

It is shown that a stochastic process described by a complex Langevin equation leads to real-time quantum mechanics. The author also derives a relation between a transition probability in the theory and a transition probability amplitude in real-time quantum mechanics in the framework of path-integral formulations. Finally, taking a harmonic oscillator case as an example, the Fokker-Planck equation is solved exactly, and a non-dissipation property of the stochastic process is pointed out.

Walter E Thirring