Quantum number

A value that specifies a property of a quantum system or distinguishes one allowed quantum state from another. Quantum numbers label discrete states and can encode quantities such as energy, angular momentum, or spin.

Quantum state: A mathematical description of a quantum system that encodes the probabilities of possible measurement outcomes. Quantum numbers distinguish possible states of a system.
Angular momentum operator: A quantum-mechanical operator that represents a component or magnitude of angular momentum. Its eigenvalues supply angular-momentum quantum numbers.
Atomic orbital: A quantum state of an electron in an atom, described by a wavefunction and quantum numbers. Its shape and energy are classified using principal, angular-momentum, and magnetic quantum numbers.
Classical state: A description of a classical system by definite values of its physical variables. Unlike classical variables, quantum-number values may be restricted to discrete alternatives.
Observable: A measurable physical quantity represented in quantum mechanics by a Hermitian operator. Many quantum numbers label possible measurement values of observables.
Commutator: An operation measuring whether two operators commute, defined as their product difference in opposite orders. Commuting observables can have shared eigenstates and simultaneous quantum-number labels.
Electron configuration: The distribution of electrons among an atom's or ion's quantum states. Quantum-number labels specify which electron states are occupied.
Continuous spectrum: A range of spectral values without gaps between its possible values. Not every quantum observable has only discrete quantum-number values.
Eigenvalue: A scalar associated with an eigenvector of a linear operator. Measured values of quantized observables are eigenvalues, often used as quantum numbers.
Rotational symmetry: Invariance of a system's laws or properties under rotations. Rotational symmetry underlies angular-momentum labels and their degeneracies.

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