I solved it!
Thank goodness! I have solved it now.
One can do the calculations in either generic Hilbert space for general rotations or in 3D real Hilbert space.
Homework Statement
Show that if a Hamiltonian H is invariant under all rotations, then the eigenstates of H are also eigenstates of L^{2} and they have a degeneracy of 2l+1.
Homework Equations
The professor told us to recall that
J: \vec{L}=(L_x,L_y,L_z)...