  For slowly varying fields the vacuum functional of a quantum field theory may
be expanded in terms of local functionals. This expansion satisfies its own
form of the Schr\"odinger equation from which the expansion coefficents can be
found. For scalar field theory in 1+1 dimensions we show that this approach
correctly reproduces the short-distance properties as contained in the
counter-terms. We also describe an approximate simplification that occurs for
the Sine-Gordon and Sinh-Gordon vacuum functionals.
