Bound and resonance states of the nonlinear Schroedinger equation in simple model systems

Details Bound and resonance states of the nonlinear Schroedinger equation in simple model systems Bound and resonance states of the nonlinear Schroedinger equation in simple model systems

2004-09-28

arxiv.org/abs/quant-ph/0409199v1

J. Phys.A 38 (2005) 1777

Physics

Quantum Physics

19 pages, 10 figures

Scientific paper

10.1088/0305-4470/38/8/013

The stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation, is studied for the cases of a single delta potential and a delta-shell potential. These model systems allow analytical solutions, and thus provide useful insight into the features of stationary bound, scattering and resonance states of the nonlinear Schroedinger equation. For the single delta potential, the influence of the potential strength and the nonlinearity is studied as well as the transition from bound to scattering states. Furthermore, the properties of resonance states for a repulsive delta-shell potential are discussed.

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