Ground State Energy of Dilute Bose Gas in Small Negative Potential Case

Abstract

It is well known that the ground state energy of a three dimensional dilute Bose gas in the thermodynamic limit is E=4 pi a rho N when the particles interact via a non-negative, finite range, spherically symmetric, two-body potential. Here, N is the number of particles, rho is the density of the gas, and a is the scattering length of the potential. In this paper, we prove the same result without the non-negativity condition on the potential, provided the negative part is small.