Two Particle States in an Asymmetric Box

Abstract

The exact two-particle energy eigenstates in an asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum are obtained. These results can be viewed as a generalization of the corresponding formulae in a cubic box obtained by Lüscher before. In particular, the s-wave scattering length is related to the energy shift in the finite box. Possible applications of these formulae are also discussed.

9 pages, typos corrected from version 2

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