  We derive a bound on the total number of negative energy bound states in a
potential in two spatial dimensions by using an adaptation of the Schwinger
method to derive the Birman-Schwinger bound in three dimensions. Specifically,
counting the number of bound states in a potential gV for g=1 is replaced by
counting the number of g_i's for which zero energy bound states exist, and then
the kernel of the integral equation for the zero-energy wave functon is
symmetrized. One of the keys of the solution is the replacement of an
inhomogeneous integral equation by a homogeneous integral equation.
