In 1995, three experimental groups succeeded to observe a Bose-Einstein condensate trapped by a magnetic harmonic potential. For the nonlinear system with a self consistent field due to atomic interaction, I solved a Schrödinger equation numerically, and compared with analytic approximations, both for repulsive and attractive interactions. When the Bose-Einstein condensate rotates, there occurs a vortex state which is an important characteristic of a Superfluid, and such vortices keep the Bose-Einstein condensate more stable for the case of attractive interaction. For atoms trapped by a double harmonic potential well, I showed that a tunnelling effect is inhibited when they have strong internal energy relative to kinetic energy.
