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Russian Physics Journal

Nonspreading quasi-classical wave packets in nonrelativistic quantum mechanics

Владимир Владимирович Белов, A. M. Rogova

Published Jun 1, 1994• 0 citations
Publisher
DOI
10.1007/bf00558707

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We discuss the propagation dynamics of nonspreading wave packets. We decompose the Hamiltonian into two parts. The first part is such that wave packets is its instantaneous eigenstate and is therefore irrelevant to the propagation of the packet. The second part is shown to be the effective Hamiltonian governing the motion of the packet both classically and quantum mechanically. Thus, analogous to Ehrenfest's theorem, nonspreading wave packets offer another view point directly connecting quantum mechanics and classical mechanics. This analysis also works for non-square-integrable packets, such as Airy packets.
We analyze the propagation dynamics of nonspreading wave packets by decomposing the Hamiltonian H into two parts: H = □(t) + H_c(t). The first part □(t) is such that Ψ(x, t) is its instantaneous eigenstate, and is therefore irrelevant to the propagation of the packet. The second part H_c(t) is shown to be the effective Hamiltonian governing the propagation dynamics of nonspreading wave packets both quantum mechanically and classically. The Ehrenfest theorem is thus based on the Hamiltonian H_c(t) connecting quantum mechanics and classical mechanics. This analysis also works for non-square-integrable packets, such as Airy packets, and explains why Airy packets can self-accelerate in free space.