### Eigenvectors of

We will do it as if we don't already know that the eigenvalues are .

where .

There are three solutions to this equation: , , and or , , and . 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. For example:

Try calculating the eigenvectors of .
You already know what the eigenvalues are.

Jim Branson 2013-04-22