The Ground State Energy of a Dilute Bose Gas

Abstract

According to a formula that was put forward many decades ago the ground state energy per particle of an interacting, dilute Bose gas at density $\rho$ is $2\pi {\hslash }^2\rho a/m$ to leading order in $\rho a^3\ll 1$, where $a$ is the scattering length of the interaction potential and $m$ the particle mass. This result, which is important for the theoretical description of current experiments on Bose-Einstein condensation, has recently been established rigorously for the first time. We give here an account of the proof that applies to nonnegative, spherically symmetric potentials decreasing faster than $1/r^3$ at infinity.

arXiv commentA few corrections to Eqs. 3.21 and 3.33--3.36 in the printed version have been made

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