The L\"{u}scher method for scattering on the lattice

The L\"{u}scher method for elastic scattering is a critical tool for understanding hadron-hadron interactions from lattice QCD. We investigate the approximations made in its applications in a simple quantum mechanical model. The quantization condition is numerically examined by including higher partial waves. Various setups used in practice are considered: cubic and elongated lattices, moving frames, and systems with integer and half-integer spin.