For 10 points, name these functions denoted Y-lm which arise when solving Laplace's equation in spherical coordinates.
The Wigner D-matrices can be expanded simply in terms of these functions. The fact that the sum of the squares of a subset of these functions equals a constant is used to prove Unsold's theorem. Applying the spin-raising operator to these functions yields their "spin-weighted" counterparts. Multiplying these functions by a factor of "r raised to the l" yields their "solid" counterparts. The simplest of these functions equals one over the square root of 4 pi. These functions of two variables can be reduced to functions of one variable by converting them to their associated Legendre polynomials. They are the eigenfunctions of the operators for the z-component of angular momentum and the square of angular momentum. The angular portion of the wavefunction of the hydrogen atom consists of these functions. For 10 points, name these functions denoted Y-lm which arise when solving Laplace's equation in spherical coordinates.
The Wigner D-matrices can be expanded simply in terms of these functions.
spherical harmonics [or associated Legendre polynomials until "Unsold's theorem" is read]