Addendum - R.A. Harris An Error in the Lecture of 3/13/06...

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Unformatted text preview: R.A. Harris An Error in the Lecture of 3/13/06 Chem 120A Spring 2006 I erred in relating the complex spherical harmonic, l=1,m=+1, and L=1, m=-1 to the real functions. The error is only a square root of 2 . What I wrote in class was correct. However the resulting functions were asymmetrical. Here is the symmetrical version. The ones in class were not normalized. These are Υ ( ,φ )= 3 sinθeiφ θ 11 8π Υ ( ,φ )= 3 sinθe−iφ θ 1−1 8π Υ ( ,φ )= 3 cosθ = 3 θ 10 4π 4π 1 Υ θ ,φ + Υ θ ,φ = ( ) 1−1( ) 2 11 1 Υ θ ,φ − Υ θ ,φ = ( ) 1−1( ) 2i 11 z r 3x 4π r 3y 4π r ...
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