DegPert Probs17 and 19

Here are some solutions for problems 17 and 19 regarding the effect of perturbations on the 2-fold degenerate 1st-excited state manifolds for the 2D infinite square well and the 2D harmonic oscillator, respectively. These problems tend to start with:
1) establishing a basis of (2) degenerate eigenvectors which span the degeneracy "manifold",
which is followed by:
2) a calculation of the matrix of the perturbation in that basis,
3) determining the eigenvalues and eigenvectors of that matrix,
and
4a) using the eigenvalues to establish the perturbed energies.
Then the last part, which is very important, and conceptually and computationally difficult:
4b) using the eigen-vectors of the matrix to establish "new" spatial (x,y) eigenvectors.