As an example, lets take the
direction to be in the
plane, between the positive
30 degrees from the x axis.
The unit vector is then
We may simply calculate the matrix
Factoring out the , the equation for the eigenvectors is.
There is an alternate way to solve the problem using rotation matrices. We take the states and rotate the axes so that the axis is where the axis was. We must think carefully about exacty what rotation to do. Clearly we need a rotation about the axis. Thinking about the signs carefully, we see that a rotation of -60 degrees moves the axis to the old axis.
Jim Branson 2013-04-22