  The spectrum of excited states observed in the finite volume of lattice QCD
is governed by the discrete symmetries of the cubic group. This finite group
permits the mixing of orbital angular momentum quanta in the finite volume. As
experimental results refer to specific angular momentum in a partial-wave
decomposition, a formalism mapping the partial-wave scattering potentials to
the finite volume is required. This formalism is developed herein for
Hamiltonian effective field theory, an extension of chiral effective field
theory incorporating the L\"uscher relation linking the energy levels observed
in finite volume to the scattering phase shift. The formalism provides an
optimal set of rest-frame basis states maximally reducing the dimension of the
Hamiltonian, and it should work in any Hamiltonian formalism. As a first
example of the formalism's implementation, lattice QCD results for the spectrum
of an isospin-2 $\pi\pi$ scattering system are analyzed to determine the $s$,
$d$, and $g$ partial-wave scattering information.
