In the following exercises 'verify' means using a hand calculator. They are
intended to confirm understanding of the theory involved. Work though one or
more examples to confirm the validity of the statement that follows.
- 1.
- Verify that the eigenvectors are normalized.
- 2.
- Verify that the eigenvectors are orthogonal to each other.
- 3.
- Verify that the eigenvalues are correct.
- 4.
- Verify that the eigenvectors diagonalize the Fock matrix.
- 5.
- Verify that the diagonal sum rule is obeyed; i.e., that the sum of the
eigenvalues is equal to the sum of the diagonal matrix elements (the trace) of
the Fock matrix.