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Register a new userHyperspherical-LOCV Approximation to Resonant BEC
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We study the ground state properties of a system of $N$ harmonically trapped bosons of mass $m$ interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle $E_0/N approx 2.5 N^{1/3} hbar omega$ and two-body contact $C_2/N approx 16 N^{1/6}sqrt{momega/hbar}$ for a Bose gas on resonance, where $omega$ is the trap frequency.
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