Wave function of a Brownian particle
نویسنده
چکیده
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 mẍ + 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 t → ∞, and (iii) its center describes a Brownian motion and so the uncertainty in the position of the particle grows without limit. PACS numbers: 05.40.+j, 03.65.-w Typeset using REVTEX ∗Electronic address: [email protected]
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تاریخ انتشار 1998