Wave function of a Brownian particle

R. M. Cavalcanti
Phys. Rev. E 58, 6807 – Published 1 November 1998
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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 m+η=F(t). 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 t, 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

Authors & Affiliations

R. M. Cavalcanti*

  • Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030

  • *Electronic address: rmc@itp.ucsb.edu

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Vol. 58, Iss. 5 — November 1998

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