  By integrating the pressure equation at the surface of a self coupled
curvilinear boundary, one may obtain asymptotic estimates of energy shifts,
which is especially useful in lattice QCD studies of nonrelativistic bound
states. Energy shift expressions are found for periodic (antiperiodic) boundary
conditions on antipodal points, which require Neumann (Dirichlet) boundary
conditions for even parity states and Dirichlet (Neumann) boundary conditions
for odd parity states. It is found that averaging over periodic and
antiperiodic boundary conditions is an effective way of removing the asymptotic
energy shifts from the boundary. Asymptotic energy shifts from boxes with self
coupled walls are also considered and shown to be effectively antipodal. The
energy shift equations are illustrated by the solution of the bounded harmonic
oscillator and hydrogen atoms.
