Nondispersive accelerating wave packets

Journal Article · Wed Jun 01 04:00:00 EDT 1994 · American Journal of Physics; (United States)

DOI:https://doi.org/10.1119/1.17510· OSTI ID:7271624

Besieris, I M ^[1]; Shaarawi, A M ^[2]; Ziolkowski, R W ^[3]

---

1. The Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 (United States)
2. Department of Engineering Physics and Mathematics, Faculty of Engineering, Cairo University, Giza (Egypt)
3. Department of Electrical and Computer Engineering, The University of Arizona, ECE Building 104, Room 422E, Tucson, Arizona 85721 (United States)

Motivated by the work of Berry and Balazs and Greenberger on the 1-D Schroedinger equation, we have investigated a class of nonspreading solutions to the 3-D Schroedinger equation involving accelerating Airy envelopes. These solutions are characterized by an asymmetric structure, in contrast to recently derived spherically symmetric packets moving with constant velocities. The field of a characteristic Airy packet extends in an oscillatory fashion behind its peak amplitude, while it quickly disappears in front of the packet's center. A particle modeled by such a packet seems to leave a wake of its field behind as it accelerates in a certain direction. On the other hand, a wave packet moving with a constant velocity has a field which is symmetrically distributed in all directions. Our work on Airy-type solutions to the 3-D Schroedinger equation has led us also to analogous solutions for the 3-D scalar wave equation.

• OSTI ID: 7271624
• Journal Information: American Journal of Physics; (United States), Journal Name: American Journal of Physics; (United States) Vol. 62:6; ISSN 0002-9505; ISSN AJPIAS
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCELERATION
AIRY FUNCTIONS
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS
WAVE PACKETS