Physics NotePublished
Soliton-like solutions to the ordinary Schroedinger equation
Michel Zamboni-Rached; Erasmo Recami
Publication details
- Authors
- Michel Zamboni-Rached; Erasmo Recami
- Type
- Physics Note
- Status
- Published
- Publication date
- 10/05/2011
- Description
- In recent times it has been paid attention to the fact that (linear) wave equations admit of ``soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than gaussian's, for describing elementary particle motion. \ In this paper we show that, {\em mutatis mutandis}, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. \ In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain finite-energy solutions. \ At last, we briefly consider solutions for a particle moving in the presence of a potential.
- Year
- 2011
- Number
- CBPF-NF-010/11
- Linked to a thesis
- No
- Linked to a grant
- No