Please answer all parts of the question. Equations 14.175, 14.172, and 14.152 are given below for reference.

14.1.8. (a) Show that the magnetic dipole Hamiltonian (14.175) yields a zero matrix element for the 3d to Is transition in hydrogen. Suggestion: Express the angular momentum operator L in terms of L+,L _, and L. (b) Show that the electric quadrupole Hamiltonian can yield a nonzero matrix element for this 3d to Is transition. Suggestion: Use the \"trick\" (14.152) to express the rst term on the right-hand side of (14.172) solely in terms of position Operators. \f-ik . re . p =- NIN. (k . fe . p + e . rk . p) - NIN. (k . fe . p - & . fk . p) (14.172)the commutator of the Hamiltonian and the position operator is given by [Ho, ]= [p2 , * ;] 2 /1 = 2 /1 in (14.152) pjihoij Pi