Dynamics of a Wavefunction for the Attractive Nonlinear Schrödinger Equation under Isotropic Harmonic Confinement Potential

Abstract

We study dynamics of a wavefunction for the nonlinear Schrödinger equation with attractive self-interaction under a harmonic potential. By use of the variance identity and a rigorous inequality, we obtain a sufficient condition for the collapse of the wavefunction. By applying this method, we investigate the dynamic stability of a trapped Bose-Einstein condensate and its dependence on the initial shape of the condensate. The result agrees qualitatively well with the results of the time-dependent variational method. We find that the anisotropy introduced in the initial state has a significant effect on the stabilization.