  The double well potential is arguably one of the most important potentials in
quantum mechanics, because the solution contains the notion of a state as a
linear superposition of `classical' states, a concept which has become very
important in quantum information theory. It is therefore desirable to have
solutions to simple double well potentials that are accessible to the
undergraduate student. We describe a method for obtaining the numerically exact
eigenenergies and eigenstates for such a model, along with the energies
obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact
solution is accessible with elementary mathematics, though numerical solutions
are required. We also find that the WKB approximation is remarkably accurate,
not just for the ground state, but for the excited states as well.
