4. Answer the following questions regarding angular momentum operators in three dimensions. a) Based on the fact that L, and Ly Hermitian operators, show that L. and L_ are Hermitian conjugate to each other. (2 pts) b) Is L_L, a Hermitian operator? Please justify your answer. (2 pts) c) Use the definition of L' and the commutator of Lx and Ly to show that L' = L_L+ + hLz + Lz. (2 pts) d) Use the conclusion of a) and c) to show that the coefficient c in the relationship L+ |l, m) = chll, m + 1) is equal to VI(l + 1) - m(m + 1). (3 pts) e) Use the conclusion of d) to show that for a given l, the largest possible m is l. (1 pt)Q4 4a) Use the definition of L+ = Lx + iLy. 4b) Yes