Phys. Rev. E 58, 6807–6809 (1998)Wave function of a Brownian particleReceived 5 May 1998; published in the issue dated November 1998 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 mx¨+ηẋ=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 t⃗∞, and (iii) its center describes a Brownian motion and so the uncertainty in the position of the particle grows without limit. © 1998 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.58.6807
DOI:
10.1103/PhysRevE.58.6807
PACS:
05.40.+j, 03.65.-w
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