Effective potentials for dilute Bose-Einstein condensates

We present a theoretical formulation of trapped, dilute Bose-Einstein condensates (BEC's) at zero temperature based on ordinary Schrodinger quantum mechanics. By a judicious choice of coordinates and of a variational trial wave function we reduce the many-atom problem to a linear Schrodinger equation that is easier to handle and interpret than the usual nonlinear Schrodinger equation of BEC theory. Ordinary quantum mechanics then reproduces, semiquantitatively, many of the main features of zero-temperature BEG, 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 Schrodinger equation. Moreover, the present procedure represents a step in a systematic alternative method for computing quantitatively accurate wave functions for trapped bosonic atoms.