Validation of the Lüscher Method on the Lattice

The L\"{u} scher method for two-particle scattering is a critical tool for connecting finite-volume spectrum with infinite-volume scattering phaseshifts. We investigate the efficacy of the method in a simple quantum mechanical model. The quantization condition is numerically examined, including the effects of higher partial waves. Various setups used in practice are explored: cubic and elongated lattices, moving frames, and systems with integer and half-integer spin.