Finite-well potential in the 3D nonlinear Schroedinger equation: Application to Bose-Einstein condensation
arXiv:cond-mat/0702281 · doi:10.1140/epjd/e2007-00006-0
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.
arXiv comment8 pages, 12 figures
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