To within a normalization factor, the product of one of these functions and an associated Laguerre polynomial gives the wavefunction of the hydrogen atom.
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.
spherical harmonics [accept associated Legendre polynomials or regular solid harmonics or irregular solid harmonics before "addition", but do not accept or prompt on any of those answers therea ter; prompt on harmonic functions]