  We analyze the initial value problem for scalar fields obeying the
Klein-Gordon equation. The standard Cauchy initial value problem for second
order differential equation is to construct a solution function in a
neighborhood of space and time form values of the function and its time
derivative on a selected initial value surface. On the characteristic surfaces
the time derivative of the solution function may be discontinuous, so the
standard Cauchy construction breaks down. For the Klein-Gordon equation the
characteristic surfaces are null surfaces. An alternative version of the
initial data needed differs from that of the standard Cauchy problem, and in
the case we discuss here the values of the function on an intersecting pair of
null surfaces comprise the necessary initial value data. We also present an
expression for the construction of a solution from null surface data; two
analogues of the quantum mechanical Hamiltonian operator determine the
evolution of the system.
