Question

Solving a problem about the eigenvalues of an operator and the probability of each outcome

Answer 1

I saw this example here: http://quantummechanics.ucsd.edu/ph130a/130_notes/node261.html#example:Lxev

I can't figure out why they set the eigenvalue to be \[\frac{ \hbar }{ \sqrt{2} }*b\]. Do they take into account that this is an angular momentum projection operator? How about solving the problem about any other operator?

Answer 2

In the example you sent,

\[ L_x = \frac{\hbar}{\sqrt{2}} \] times the matrix.

and the eigenvalue they are seeking is really $a$. They've moved the $\hbar$ factor to the other side and defined $b$ to simplify the algebra.