1999/10/31 by Elliott H. Lieb, Jakob Yngvason
Physics and Astronomy · Mathematics · #math-ph #cond-mat #math.MP #msc:81V70 #msc:35Q55 #msc:46N50
published as Published in {\it Differential Equations and Mathematical Physics, University of Alabama, Birmingham, 1999}, R. Weikard and G. Weinstein, eds., 271-282 Amer. Math. Soc./Internat. Press (2000). eds., 271-282 Amer. Math. Soc./Internat. Press (2000) · A few corrections to Eqs. 3.21 and 3.33--3.36 in the printed version have been made
arxiv created 2000/08/20 · arxiv updated 2009/11/30
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 ρ is 2πℏ2ρa/m to leading order in ρa3≪ 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/r3 at infinity.