  In the eighties, Schroder studied a quantum mechanical model where the
stationary states of Schrodinger's equation obey nonlocal boundary conditions
on a circle in the plane. For such a problem, we perform a detailed one-loop
calculation for three choices of the kernel characterizing the nonlocal
boundary conditions. In such cases, the zeta(0) value is found to coincide with
the one resulting from Robin boundary conditions. The detailed technique here
developed may be useful for studying one-loop properties of quantum field
theory and quantum gravity if nonlocal boundary conditions are imposed.
