The Ground State Energy of a Dilute Bose Gas

Details The Ground State Energy of a Dilute Bose Gas The Ground State Energy of a Dilute Bose Gas

1999-10-20

arxiv.org/abs/math-ph/9910033v2

Published in {\it Differential Equations and Mathematical Physics, University of Alabama, Birmingham, 1999}, R. Weikard and G.

Physics

Mathematical Physics

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

Scientific paper

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 $2\pi\hbar^2\rho a/m$ 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.

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