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Nonspreading wave packets
Abstract
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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Cited by
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Kavokin, A. V., Baumberg, J. J., Malpuech, G., & Laussy, F. P. (2017) · doi:10.1093/oso/9780198782995.001.0001 · Cited by 326
Experimental Observation of a Photon Bouncing Ball
Della Valle, G., Savoini, M., Ornigotti, M., Laporta, P., Foglietti, V., Finazzi, M., Duò, L., & Longhi, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.180402 · Cited by 57
Metadata
- Authors
- Berry, M. V., & Balazs, N. L.
- Venue
- American Journal of Physics
- Published
- 1979-03-01
- Volume
- 47
- Issue
- 3
- Pages
- 264-267
- ISSN
- 0002-9505 (ISSN-L)
- 1943-2909
- OpenAlex
- W1994554237
- Cited by
- 1,581
- References
- 0
- FWCI
- 0.90
- Type
- journal article
- Language
- en
- Open access
- closed
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- Berry, M. V., & Balazs, N. L. (1979). Nonspreading wave packets. American Journal of Physics. https://doi.org/10.1119/1.11855
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