Homework Statement
Consider a molecule with an electric dipole moment d. The Hamiltonian of a molecule in the external electric field E is: \hat{H} = \frac{\hat{L^2}}{2I} - dE \cos{\theta}, where the polar angle \theta characterises the orientation of the molecule. (We have chosen the field...
Sorry I forgot to mention this is for l=1.
Okay, but I used L_z eigenvalues of m\hbar, where m=-1,0,1 in this case, and used L_x=\frac{1}{2}(L_+ + L_- ). I have called the z component the one in which is certain, so how can the x component squared in this case have the same eigenvalues as the z...
Homework Statement
Calculate the eigenvalues of the L_x^2 matrix.
Calculate the eigenvalues of the L_z^2 matrix.
Compare these and comment on the result.
Homework Equations
L_x=\frac{1}{2}(L_+ + L_- )
The Attempt at a Solution
I have derived eigenvalues for each: 0 and \hbar^2...