Having looked at solutions that are obtained exactly or through perturbation theory, we now consider cases where we have to resort to some unique approximation schemes, both for scattering and for bound states. In relation to the bound states we introduce the WKB approximation, and the variational method. For scattering at high energies we introduce the eikonal approximation, which is closely allied to the WKB method.
We begin with the Schrödinger equation in one dimension,
which we write as
If V(x) is a constant, equal to V0, then in that ...