Two Particle States in an Asymmetric Box and the Elastic Scattering Phases
Abstract
The exact two-particle energy eigenstates in a generic 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 for both D4 and D2 symmetry. These results can be viewed as a generalization of the corresponding formulae in a cubic box obtained by L\"uscher 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.
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