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 $E^{\frac{1}{2}}\delta \mathrm{}\left(E\right)\mathrm{}{v}^{-\frac{1}{3}}$, where $\delta$ is the corresponding phase shift. Application of this result to the many-particle problem is discussed.