# Bohmian trajectories of Airy packets

## Abstract

The discovery of Berry and Balazs in 1979 that the free-particle Schrödinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schrödinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the corresponding Bohmian trajectories. It is shown that by using general space–time transformations, these trajectories can display a unique variety of cases depending upon the initial position of the individual particle in the Airy wave packet. Further, we report here a myriad of nontrivial Bohmian trajectories associated to the Airy wave packet. These new features are worth introducing to the subject’s theoretical folklore in light of the fact that the evolution of a quantum mechanical Airy wave packet governed by the Schrödinger equation is analogous to the propagation of a finite energy Airy beam satisfying the paraxial equation. Numerous experimental configurations of optics and atom physics have shown that the dynamics of Airy beams dependsmore »

- Authors:

- Science Department, Harvard-Westlake School, 3700 Coldwater Canyon, Studio City, 91604 (United States)
- (United States)
- Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid (Spain)

- Publication Date:

- OSTI Identifier:
- 22403387

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 348; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMIC PHYSICS; EXPERIMENTAL DATA; MATHEMATICAL SOLUTIONS; OPTICS; QUANTUM MECHANICS; SCHROEDINGER EQUATION; SPACE-TIME; TIME DEPENDENCE; TRAJECTORIES; WAVE PACKETS

### Citation Formats

```
Nassar, Antonio B., E-mail: anassar@hw.com, Department of Sciences, University of California, Los Angeles, Extension Program, 10995 Le Conte Avenue, Los Angeles, CA 90024, and Miret-Artés, Salvador.
```*Bohmian trajectories of Airy packets*. United States: N. p., 2014.
Web. doi:10.1016/J.AOP.2014.05.021.

```
Nassar, Antonio B., E-mail: anassar@hw.com, Department of Sciences, University of California, Los Angeles, Extension Program, 10995 Le Conte Avenue, Los Angeles, CA 90024, & Miret-Artés, Salvador.
```*Bohmian trajectories of Airy packets*. United States. doi:10.1016/J.AOP.2014.05.021.

```
Nassar, Antonio B., E-mail: anassar@hw.com, Department of Sciences, University of California, Los Angeles, Extension Program, 10995 Le Conte Avenue, Los Angeles, CA 90024, and Miret-Artés, Salvador. Mon .
"Bohmian trajectories of Airy packets". United States. doi:10.1016/J.AOP.2014.05.021.
```

```
@article{osti_22403387,
```

title = {Bohmian trajectories of Airy packets},

author = {Nassar, Antonio B., E-mail: anassar@hw.com and Department of Sciences, University of California, Los Angeles, Extension Program, 10995 Le Conte Avenue, Los Angeles, CA 90024 and Miret-Artés, Salvador},

abstractNote = {The discovery of Berry and Balazs in 1979 that the free-particle Schrödinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schrödinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the corresponding Bohmian trajectories. It is shown that by using general space–time transformations, these trajectories can display a unique variety of cases depending upon the initial position of the individual particle in the Airy wave packet. Further, we report here a myriad of nontrivial Bohmian trajectories associated to the Airy wave packet. These new features are worth introducing to the subject’s theoretical folklore in light of the fact that the evolution of a quantum mechanical Airy wave packet governed by the Schrödinger equation is analogous to the propagation of a finite energy Airy beam satisfying the paraxial equation. Numerous experimental configurations of optics and atom physics have shown that the dynamics of Airy beams depends significantly on initial parameters and configurations of the experimental set-up.},

doi = {10.1016/J.AOP.2014.05.021},

journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = ,

volume = 348,

place = {United States},

year = {2014},

month = {9}

}