Associated Legendre Polynomials Lecture (20 minutes)

Central Forces Notes Section 25

  • The Associated Legendre functions are defined and it is explained that these functions solve the general case in which m is not equal to 0. The Associated Legendre functions are not derived explicitly in the name of expediency.
  • Some of the properties of the Associated Legendre functions are also demonstrated, including:
    • orthogonality and the inner product
    • the normalization constant is shown
    • the Rodriguez formula
    • the fact that for $m>\ell$, the Associated Legendre Polynomials are equal to 0. This fact should be a one-step argument based on Rodriguez formula and is the basis for the restriction on the quantum numbers that $m<\ell$.

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