These functions can be rescaled using Schmidt semi-normalization. The standard proof of Unsöld's theorem relies on these functions' namesake addition theorem. Applying the spin raising and lowering operators to these functions gives their "spin-weighted" variety, which can be used to  nd multipole solutions of Maxwell's equations in a source-free region. The Slater integral of the product of three of these functions is proportional to the product of two Wigner three-j symbols. The simplest of these functions equals the square root of one over four pi. They are the eigenfunctions of the L-squared and L-sub-z operators. To within a normalization factor, the product of one of these functions and an associated Laguerre polynomial gives the wavefunction of the hydrogen atom. For 10 points, identify these functions den
These functions can be rescaled using Schmidt semi-normalization. The standard proof of Unsöld's theorem relies on these functions' namesake addition theorem. Applying the spin raising and lowering operators to these functions gives their "spin-weighted" variety, which can be used to  nd multipole solutions of Maxwell's equations in a source-free region. The Slater integral of the product of three of these functions is proportional to the product of two Wigner three-j symbols. The simplest of these functions equals the square root of one over four pi. They are the eigenfunctions of the L-squared and L-sub-z operators. To within a normalization factor, the product of one of these functions and an associated Laguerre polynomial gives the wavefunction of the hydrogen atom. For 10 points, identify these functions denoted Y-sub-l-super-m that solve the angular part of Laplace's equation in their namesake coordinate system.
These functions can be rescaled using Schmidt semi-normalization.