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