Orbital angular momentum

Orbital angular momentum is the angular momentum associated with a particle’s position and linear momentum, classically given by their cross product. In quantum mechanics, its components are operators with quantized angular-momentum states.

Angular momentum operator: A quantum operator whose eigenvalues describe angular momentum along specified axes. Orbital angular momentum is one realization of this operator, built from position and momentum.
Position vector: A vector specifying an object's location relative to a chosen origin. Its displacement from the origin is one factor in the cross product defining orbital angular momentum.
Atomic orbital: A one-electron quantum state in an atom, described by spatial wavefunctions and quantum numbers. Its angular shape and orbital quantum number encode orbital angular momentum.
Total angular momentum: The conserved angular momentum formed by combining a system's orbital and intrinsic contributions. It combines orbital angular momentum with spin rather than describing spatial motion alone.
Canonical commutation relation: The quantum relation between position and momentum operators, expressed by their commutator. These commutators generate the noncommuting components of orbital angular momentum.
Linear momentum: A vector quantity equal to mass times velocity in classical mechanics and represented by an operator in quantum mechanics. It supplies the second factor in the defining expression r × p.
Atomic spectroscopy: The study of atoms through their absorption and emission of electromagnetic radiation. Orbital angular momentum helps determine atomic energy levels and spectral transitions.
Orbital angular momentum of light: The angular momentum associated with the spatial phase structure of an electromagnetic field. It is a field-based counterpart, with helical wavefronts carrying orbital angular momentum.
Spherical harmonics: Angular functions on a sphere that form eigenfunctions of the squared orbital angular momentum operator. They encode orbital angular momentum in the angular part of three-dimensional wavefunctions.
Cross product: A vector operation in three dimensions that produces a vector perpendicular to two input vectors. It determines orbital angular momentum's direction and classical magnitude.

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