Problem 4.17: Use the shift operator once to generate the function given by l = 2 and mi = 1. Check your result against table 3.2. 4.17 Verify that successive application of l_ to Wu with l = 2 in eqn 4.32 generates the five normalized spherical harmonics Y,m as set out in Table 3.2 Table 3.2 Spherical harmonics
1
Ym(0,) mi 0 1/2 r 1/2 0 Z(3/r)1/2 coSA YBW 301 1381070 1 +(3/2)1/2 sin Oe*ip 0 4(5/r)1/2(3 cos^2 -1) 1 +(15/2r)1/2 cos & sin Getip 2 4(15/2T)1/2 sin^2(0)e^2ip 0 4(7/r)1/2(2 - 5 sin^2(0))cos^9 1 +(21/T)1/2(5 cos^2 - 1)sin^9e^ie 2 4(105/2T)1/2 cos(0)sin^2(0)e^2ip 3 +(35/tt)1/2 sin^3(0)e^3ip
0
1
2
3