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Vector Spherical harmonics/spherical coordinates question

  1. Jan 2, 2010 #1
    Arfken and Weber lists some of the Vector spherical harmonics in spherical coordinates, and I'm puzzled that one has no radial component. Specifically, $Y(j =1, l=1, m = 0) = i \sqrt[3/(8 \Pi)] sin(\theta) \^{phi} $

    To Cartesian components of the vector, it seems you need an r component of the vector in spherical coordinates. Since Y110 only has a phi component, does this mean that the Y110 spherical harmonic is a vector of length zero in cartesian coordinates? If so, why is there even a magnitude in the phi component of the vector? And if so, is Y110 only useful if combined with other vector spherical harmonics?

    Thanks in advance.
  2. jcsd
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