Given the expression for spherical harmonics Y"(0, $) and Rodrigues formula: Y° (8,$) = 21 + 1 P(cos 0), 1 d' P,(x) = (x² – 1)'. 2'!! dx (a) Find the expression of Y (0, 4) (b) Express Y in Cartesian coordinates
Given the expression for spherical harmonics Y"(0, $) and Rodrigues formula: Y° (8,$) = 21 + 1 P(cos 0), 1 d' P,(x) = (x² – 1)'. 2'!! dx (a) Find the expression of Y (0, 4) (b) Express Y in Cartesian coordinates
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Transcribed Image Text:Given the expression for spherical harmonics Y" (8, 4) and Rodrigues formula:
Y°(0, $) =
21 +1
P((cos 0),
1 d'
P,(x)
2'i dxi (x² – 1)!.
(a)
Find the expression of Y§(8, 4)
(b)
Express Y in Cartesian coordinates
(c) Now using
L4Y"(0,4) = ħ/I(1 + 1) – m(m ± 1)Y™±'(0,$),
cos e a
sin e apl
L = thetio
and the expression of Y (0, 4) obtained in 4(a), find Y"(, 4).
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