  We describe the application of the quantum mechanical bootstrap to the
solution of one-dimensional scattering problems. By fixing a boundary and
modulating the Robin parameter of the boundary conditions we are able to
extract the reflection coefficient for various potentials and compare to
physical expectations. This includes an application of semidefinite programming
to solving a half-line Schrodinger problem with arbitrary Robin boundary
conditions. Finally, the WKB approximation is used to numerically determine the
scattering behavior of the exponential potential of Liouville theory.
