  The covariant Klein-Gordon equation requires twice the boundary conditions of
the Schrodinger equation and does not have an accepted single-particle
interpretation. Instead of interpreting its solution as a probability wave
determined by an initial boundary condition, this paper considers the
possibility that the solutions are determined by both an initial and a final
boundary condition. By constructing an invariant joint probability distribution
from the size of the solution space, it is shown that the usual measurement
probabilities can nearly be recovered in the non-relativistic limit, provided
that neither boundary constrains the energy to a precision near hbar/T (where T
is the time duration between the boundary conditions). Otherwise, deviations
from standard quantum mechanics are predicted.
