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