  The Dirichlet problem on a bounded planar domain is more readily understood
and solved for the Laplace operator than it is for a Schrodinger operator. When
the potential function is small, we might hope to approximate the solution to
the Schrodinger equation with the solution to the Laplace equation. In this
vein we develop a series expansion for the solution and give explicit bounds on
the error terms when truncating the series. We also examine a handful of
examples and derive similar results for the Green function and
Dirichlet-to-Neumann map.
