Abstract
We present a theoretical formulation of trapped, dilute Bose-Einstein condensates (BEC's) at zero temperature based on ordinary Schr\"odinger quantum mechanics. By a judicious choice of coordinates and of a variational trial wave function we reduce the many-atom problem to a linear Schr\"odinger equation that is easier to handle and interpret than the usual nonlinear Schr\"odinger equation of BEC theory. Ordinary quantum mechanics then reproduces, semiquantitatively, many of the main features of zero-temperature BEC, including the critical number of atoms in a condensate with negative scattering length. The procedure is similar in results, but completely different in spirit, to recent variational approaches to solving the nonlinear Schr\"odinger equation. Moreover, the present procedure represents a step in a systematic alternative method for computing quantitatively accurate wave functions for trapped bosonic atoms.
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