Two Particle States in a Box and the s-Matrix in Multi-Channel Scattering
Abstract
Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions. A relation between the exact energy eigenvalue in the box and the two-channel S-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known L\"uscher's formula which establishes a similar relation in elastic scattering.
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