For the next four problems, you will be considering the electron in state described by the wave funCtiOIl $42_2. (c) (4 pts) What are the values of n, l, m, and jmax? (d) (8 pts) Apply the raising operator L+ in spherical coordinates to this wave function. Use A?" zhx/l(l+1)m(mi1):hx/(quleimll) to normalize. Verify that the result is what you would expect. (e) (8 pts) Apply the angular momentum operator L2 in spherical coordinates to this wave function. Explain the result and discuss whether it is what you would expect. (f) (4 pts) Apply the angular momentum operator LZ in spherical coordinates to this wave function. Explain the result and discuss whether it is what you would expect. For reference: 15 Y2-2 ( 0, 0 ) = -2id . sin2 0 4 2 TT 15 Y2-' (0, $ ) = e -id . sin 0 . cos 0 2 2 TT Y2 (0, $ ) = 1 . (3 cos2 0 - 1) TT 15 Y2 (0, 0) = - . el9 . sin 0 . cos 0 2 V 2 TT 15 Y2 (0, 0) = e2id . sin2 0 4 2 TT