  We investigate how quantum bound states bounce from a hard surface. Our
analysis has applications to ab initio calculations of nuclear structure and
elastic deformation, energy levels of excitons in semiconductor quantum dots
and wells, and cold atomic few-body systems on optical lattices with sharp
boundaries. We develop the general theory of elastic reflection for a composite
body from a hard wall. On the numerical side we present ab initio calculations
for the compression of alpha particles and universal results for two-body
states. On the analytical side we derive a universal effective potential that
gives the reflection scattering length for shallow two-body states.
