  Elastic quantum bound-state reflection from a hard-wall boundary provides
direct information regarding the structure and compressibility of quantum bound
states. We discuss elastic quantum bound-state reflection and derive a general
theory for elastic reflection of shallow dimers from hard-wall surfaces using
effective field theory. We show that there is a small expansion parameter for
analytic calculations of the reflection scattering length. We present a
calculation up to second order in the effective Hamiltonian in one, two, and
three dimensions. We also provide numerical lattice results for all three cases
as a comparison with our effective field theory results. Finally, we provide an
analysis of the compressibility of the alpha particle confined to a cubic
lattice with vanishing Dirichlet boundaries.
