Using Equation 4.32, find Y (,) and Y 2 3 (,) . (You can take

Using Equation 4.32, find Y^ℓ_ℓ (θ,ϕ) and Y²₃ (θ,ϕ) . (You can take P²₃ from Table 4.2, but you’ll have to work out P^ℓ_ℓ from Equations 4.27 and 4.28.) Check that they satisfy the angular equation (Equation 4.18), for the appropriate values of and m.

Equation 4.32

Table 4.2

Some associated Legendre functions, P^m_ℓ (cosθ) : (a) functional form, (b) graphs of r = |P^m_ℓ (cosθ)| (in these plots r tells you the magnitude of the function in the direction θ; each figure should be rotated about the z axis).

Equation 4.18

Transcribed Image Text:

Y" (0,0) = (2e + 1) (e-m) imdb p (cos), 4TC (l+ m)! (4.32)