We show that for a wave ψ in the form of an Airy function the probability density ‖ψ‖2 propagates in free space without distortion and with constant acceleration. This ’’Airy packet’’ corresponds classically to a family of orbits represented by a parabola in phase space; under the classical motion this parabola translates rigidly, and the fact that no other curve has this property shows that the Airy packet is unique in propagating without change of form. The acceleration of the packet (which does not violate Ehrenfest’s theorem) is related to the curvature of the caustic (envelope) of the family of world lines in spacetime. When a spatially uniform force F (t) acts the Airy packet continues to preserve its integrity. We exhibit the solution of Schrödinger’s equation for general F (t) and discuss the motion for some special forms of F (t).
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March 1979
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March 01 1979
Nonspreading wave packets
M. V. Berry;
M. V. Berry
H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
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N. L. Balazs
N. L. Balazs
State University of New York at Stony Brook, Stony Brook, New York 11794
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Am. J. Phys. 47, 264–267 (1979)
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M. V. Berry, N. L. Balazs; Nonspreading wave packets. Am. J. Phys. 1 March 1979; 47 (3): 264–267. https://doi.org/10.1119/1.11855
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