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The European Physical Journal D

, Volume 42, Issue 2, pp 279–286 | Cite as

Finite-well potential in the 3D nonlinear Schrödinger equation: application to Bose-Einstein condensation

  • S. K. AdhikariEmail author
Laser Cooling and Quantum Gas
  • 128 Downloads

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.

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 

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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Instituto de Física Teórica, UNESP, São Paulo State UniversitySão PauloBrazil

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