Generalized nonpolynomial Schrödinger equations for matter waves under anisotropic transverse confinement
نویسنده
چکیده
Starting from the three-dimensional Gross-Pitaevskii equation (3D GPE) we derive a 1D generalized nonpolynomial Schrödinger equation (1D g-NPSE) which describes the dynamics of Bose-Einstein condensates under the action of a generic potential in the longitudinal axial direction and of an anisotropic harmonic potential in the transverse radial direction. This equation reduces to the familiar 1D NPSE [Phys. Rev. A 65, 043614 (2002)] in the case of isotropic transverse harmonic confinement. In addition we show that if the longitudinal potential models a periodic optical lattice the 3D GPE can be mapped into a 1D generalized discrete nonpolynomial Schrödinger equation (1D g-DNPSE). Generalized nonpolynomial Schrödinger equations 2
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