27 May 2002
Physics Letters A 298 (2002) 7–17
Wave packets and Bohmian mechanics in the kicked rotator
Gary E. Bowman
Department of Physics and Astronomy, Northern Arizona University, PO Box 6010, Flagstaff, AZ 86011, USA
Received 2 May 2001; received in revised form 13 November 2001; accepted 16 November 2001
Communicated by P.R. Holland
Quantum-mechanical kicked-rotator wave packets are studied using Bohmian mechanics and a novel numerical approach.
A method for extending the results into the classical regime is developed. A clear physical picture of packet behavior, including
a new expression for packet spread times, emerges.
2002 Elsevier Science B.V. All rights reserved.
PACS: 03.65.-w; 05.45.Mt; 05.45.Pq
Keywords: Quantum chaos; Bohmian mechanics; Wave packets; Spread times
The tools of Bohm’s causal interpretation of quan-
tum mechanics (Bohmian mechanics), including the
concepts of particle and trajectory, hold the prospect
of generating new insights into quantum systems.
For example, the tunneling of wave packets through
smooth potential barriers was recently analyzed us-
ing Bohmian mechanics, resulting in a physically clear
picture in terms of forces on, and energies of, members
of the Bohmian ensemble .
Since the kicked rotator is an archetype of both
classical and quantum chaos, the behavior of wave
packets in the quantum rotator is of intrinsic interest.
Using Bohmian mechanics, along with a novel numer-
ical approach, we will investigate this behavior, and
compare it with that of the corresponding classical ro-
tator. While much of our work is framed in the context
E-mail address: firstname.lastname@example.org (G.E. Bowman).
of Bohmian mechanics, we emphasize that our conclu-
sions regarding packet behavior are more general, and
must also hold in “standard” quantum mechanics.
The study of chaos in Bohmian mechanics has
developed considerably in the last few years—an early
discussion appears in , while a concise review has
appeared recently . Some authors have discussed
the conditions that may lead to Bohmian chaos ,
while others focus on speciﬁc systems [5–11] such as
the “cat map” , a hydrogen atom in an oscillating
electric ﬁeld , and the Hénon–Heiles oscillator .
Schwengelbeck and Faisal  have examined the
Bohmian kicked rotator. They compare the behavior
of an initially uniform distribution of classical rotator
trajectories with that of an identical initial distribution
of Bohmian rotator trajectories. The Bohmian trajec-
tories do not exhibit chaos, while the classical trajec-
tories do. Malik and Dewdney  concur with this
lack of chaos in the rotator. Starting with various initial
states—the ground state, superpositions of two eigen-
states, and Gaussian packets—they fail to ﬁnd diver-
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