The routine getallEs() from the previous problem finds for us the unknown energies for the Schrödinger equation. Given these energies, the Schrödinger equation becomes an ordinary differential equation (ODE) which we may solve with rk4p480().
Three things must be done to the raw output of rk4p480 before we can return the final wave functions. First, as discussed in lecture, numerical stability demands that we integrate Schrödinger's equation both inward and outward and match the solutions at a given matching point. Second, rk4p480() provides values only on every other data-point k and so we must interpolate to find values for the remaining points. Finally, we must normalize the wave functions.