###

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