Unformatted text preview: 2 2 = + + m l l d d d d . The solution is ) (cos ) ( m l lm AP = , with ) ( ) 1 ( ) (   2 /  2 x P dx d x x P l m m m l = and l l l l x dx d l x P ) 1 ( ! 2 1 ) ( 2 = with l = 0, 1, 2, and m = l , l +1, , + l . Spherical Harmonics: The normalized wave functions ) (cos )!  ( 4 )!  )( 1 2 ( ) ( ) ( ) , ( m l im m lm lm P e m l m l l Y + + + = = , where = (1) m for m 0 and = 1 for m &lt; 0. The Y lm form an orthonormal set, [ ] ' ' 2 0 0 ' ' sin ) , ( ) , ( mm ll lm m l d d Y Y = . Legendre Polynomials...
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 Spring '07
 FIELDS
 mechanics, Spherical Harmonics, Sin, Legendre polynomials, Associated Legendre function

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