ua nt - p h / 04 09 19 9 v 1 2 8 Se p 20 04 Bound and resonance states of the nonlinear Schrödinger equation in simple model systems
نویسنده
چکیده
The stationary nonlinear Schrödinger 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 Schrödinger 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. Submitted to: J. Phys. A: Math. Gen. PACS numbers: 03.65.Ge, 03.65.Nk, 03.75-b, 05.45.Yv Bound and resonance states of the nonlinear Schrödinger equation in simple model systems2
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