Finite-well potential in the 3D nonlinear Schrödinger equation: application to Bose-Einstein condensation
Instituto de Física Teórica, UNESP, São Paulo State University, 01-, 405-900 São Paulo, Brazil
Corresponding author: a email@example.com
Revised: 11 October 2006
Published online: 17 January 2007
Using variational and numerical solutions we show that stationary negative-energy localized (normalizable) bound states can appear in the three-dimensional nonlinear Schrödinger equation with a finite square-well potential for a range of nonlinearity parameters. Below a critical attractive nonlinearity, the system becomes unstable and experiences collapse. Above a limiting repulsive nonlinearity, the system becomes highly repulsive and cannot be bound. The system also allows nonnormalizable states of infinite norm at positive energies in the continuum. The normalizable negative-energy bound states could be created in BECs and studied in the laboratory with present knowhow.
PACS: 45.05.+x – General theory of classical mechanics of discrete systems / 05.45.-a – Nonlinear dynamics and chaos / 03.75.Hh – Static properties of condensates; thermodynamical, statistical, and structural properties
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007