Abstract
Using the Hamiltonian of Caldirola [Nuovo Cimento 18, 393 (1941)] and Kanai [Prog. Theor. Phys. 3, 440 (1948)], we study the time evolution of the wave function of a particle whose classical motion is governed by the Langevin equation We show in particular that if the initial wave function is Gaussian, then (i) it remains Gaussian for all times, (ii) its width grows, approaching a finite value when and (iii) its center describes a Brownian motion and so the uncertainty in the position of the particle grows without limit.
- Received 5 May 1998
DOI:https://doi.org/10.1103/PhysRevE.58.6807
©1998 American Physical Society