The raising and lowering operators change the value of m by one unit: where A m

Question:

The raising and lowering operators change the value of m by one unit:

where A^m_ℓ and B^m_ℓ are constants. Question: What are they, if the eigenfunctions are to be normalized? First show that L^-₊ is the hermitian conjugate of L± (since L_x and L_y are observables, you may assume they are hermitian…but prove it if you like); then use Equation 4.112.