Selection rule

A condition that determines whether a transition between quantum states can occur or is suppressed. Selection rules arise from transition operators, symmetries, and conservation laws.

Transition dipole moment: The matrix element of the electric dipole operator between two quantum states, governing the strength of an electric-dipole transition. Electric-dipole selection rules follow from whether this matrix element vanishes.
Quantum state: A mathematical description encoding the measurable properties and probabilities of a quantum system. Selection rules compare pairs of these states.
Atomic spectroscopy: The study of light emitted or absorbed by atoms, used to infer their structure and properties. Atomic line patterns are classified by the transitions selection rules permit.
Allowed transition: A transition with a nonzero matrix element under the selection rules for a specified interaction. It is the direct counterpart of a transition excluded at that interaction's leading order.
Parity (physics): A quantum number describing how a state transforms under spatial inversion. Parity changes constrain which states can be connected by operators of definite parity.
Quantum number: A value used to label a quantum state or a conserved property of a quantum system. Rules are often stated as permitted changes in these labels.
Hydrogen spectral series: Groups of hydrogen emission or absorption lines associated with transitions to or from a shared energy level. Selection rules determine which level-to-level lines appear in these series.
Electric quadrupole transition: A radiative transition driven by the electric quadrupole component of the light–matter interaction. It can occur when the stronger electric-dipole transition is forbidden.
Angular momentum operator: An operator representing a component or magnitude of angular momentum in quantum mechanics. Its tensor properties impose restrictions on changes in angular momentum.
Symmetry in physics: A transformation that leaves the laws or relevant properties of a physical system unchanged. Symmetries explain why many transition matrix elements vanish.

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