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physica status solidi (b)

A Monte Carlo method for propagating multi‐dimensional wave packets

Markus Schröder, Ulrich Kleinekathöfer

Published Jun 22, 2004• 2 citations
Publisher

Abstract

Abstract A method for propagating multi‐dimensional wave packets in time using a product ansatz for the wave function is presented. Other than in the time‐dependent Hartree approach which is based on a variational scheme, the current method is based on the stochastic Ito calculus. The correlations between the different one‐dimensional wave functions are taken into account via stochastic processes such that on average the original Schrödinger equation is reproduced. Numerical tests of the proposed scheme have been performed in two and four dimensions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200404787

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We present a path-integral solution for the exact propagation of the Wigner distribution in phase space, which is an improved version of results obtained [Maslov, Bertrand, Combe, and co-workers, J. Sov. Math. 13, 315 (1980); 19, 55 (1982); Lett. Math. Phys. 7, 327 (1983); Physica 124A, 561 (1984)] and is suitable for Monte Carlo simulations. The trajectories involved are purely stochastic processes exhibiting discontinuous jumps in momentum. The applicability of the method is demonstrated for scattering at a one-dimensional barrier.