1979/03/01 by Marsha Berry, N. L. Balázs · 2 citations
Physics and Astronomy · Mathematics · #Relativity and Gravitational Theory #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Physics #Wave packet #Parabola #Airy function #Caustic (mathematics) #Envelope (radar) #Acceleration #Constant (computer programming) #Classical mechanics #Spacetime #Curvature #Phase space #Motion (physics) #Distortion (music) #Mathematical analysis #Mathematical physics #Quantum mechanics #Optics #Geometry #Mathematics #Telecommunications
paper · doi:10.1119/1.11855
openalex publication_date 1979/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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).