Eur. Phys. J. D 42, 279-286 (2007)
https://doi.org/10.1140/epjd/e2007-00006-0

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 adhikari@ift.unesp.br

Received: 3 February 2006
Revised: 11 October 2006
Published online: 17 January 2007

Abstract

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.