We will do it as if we don't already
know that the eigenvalues are
There are three solutions to this equation:
These are the eigenvalues we expected for
For each of these three eigenvalues, we should go back and find the
corresponding eigenvector by using the matrix equation.
Up to a normalization constant, the solutions are:
We should normalize these eigenvectors to represent one particle.
Try calculating the eigenvectors of .
You already know what the eigenvalues are.