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Fortschritte der Physik

Interference acceleration of a free particle

Joachim Dahl, A. Wolf, Wolfgang P. Schleich

Published Oct 11, 2004• 8 citations
Publisher

Abstract

Abstract We compare and contrast classical and quantum dynamics of a free particle initially prepared in an s‐wave. Due to the wave nature of quantum theory the particle experiences an acceleration which depends on the number of space dimensions.
DOI
10.1002/prop.200410182

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We use a Markovian master equation to solve for the dynamics of a free particle damped by the coupling of its coordinate to a bath of harmonic oscillators. In the coordinate basis the reduced density matrix for the free particle tends to be diagonalized. Considering the evolution of an initial superposition of two plane waves, we find that the interference-pattern fringe contrast is decreased by the damping. However, for fixed times and sufficiently large damping, the fringe contrast increases with increasing damping. Considering an initial coordinate-space Gaussian wave function, we find that for sufficiently large damping the coupling to the environment models a quantum measurement of the particle's coordinate.
In this Brief Report we discuss a solution of the free-particle Schr\"odinger equation in which the time and space dependence are not separable. The wave function is written as a product of exponential terms, Hermite polynomials, and a phase. The peaks in the wave function decelerate and then accelerate around t=0t=0t=0. We analyze this behavior within both a quantum and a semiclassical regime. We show that the acceleration does not represent true acceleration of the particle but can be related to the envelope function of the allowed classical paths. Comparison with other ``accelerating'' wave functions is also made. The analysis provides considerable insight into the meaning of the quantum wave function.