Energy Level Shifts in a Large Enclosure

Abstract

It is proved that for a particle enclosed in a large box, a potential shifts the energy levels by an amount which, as the volume v of the enclosure tends to infinity in a suitable manner, becomes proportional to ${E}^{\frac{1}{2}}\ensuremath{\delta}(E){v}^{\ensuremath{-}\frac{1}{3}}$, where $\ensuremath{\delta}$ is the corresponding phase shift. Application of this result to the many-particle problem is discussed.