Abstract
Based on Bose-Einstein condensation in minimized momentum state, the optimization criterion of potential is studied for trapped weakly interacting Bose gas according to Thomas-Fermi approximation. A criterion for the validity of potential and the limited atom number loaded in a power law attractive potential well for ultra-cold weakly interacting Bose atom gas is derived. The criterion gives the required potential field strength when the loaded atom number is fixed, or the limited atom number when the potential field strength is given, and then, the best ranges of potential field strength are obtained, for attractive interaction and repulsive interaction, respectively.
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