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A one-electron wavefunction or basis function used in exact one-electron atoms and approximate many-electron descriptions; it is not a classical electron trajectory.
Orbitals are not classical electron trajectories and are representation-dependent ingredients of atomic and molecular models.
wp-physics-atomic_orbitaliupac-atomic-orbitalnist-atomic-statesEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
In many-electron atoms, orbitals are basis or mean-field functions used to construct antisymmetric states; they are not separately exact electron states in general.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-atomic_orbitalwp-physics-atomic_hamiltoniannist-atomic-spectroscopyThis is an authored directed relation from the source endpoint to the target endpoint.
For one-electron atoms, stationary wavefunctions are exact atomic orbitals within the chosen Hamiltonian.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-atomic_orbitalwp-physics-one_electron_atomnist-hydrogenThis is an authored directed relation from the source endpoint to the target endpoint.
Hydrogenic and central-field orbitals separate into radial functions and spherical harmonics.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-spherical_harmonicpdg-2026-mathematical-toolsnist-atomic-spectroscopywp-physics-atomic_orbitaliupac-atomic-orbitalnist-atomic-statesEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Electron configurations record occupations of a chosen orbital or subshell basis; they are state descriptions, not material assemblies of orbitals.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-electron_configurationThis is an authored directed relation from the source endpoint to the target endpoint.
In hydrogenic and central-field classifications, one-electron orbitals sharing the principal quantum number are grouped into a shell; a shell is a state classification, not a material composite.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-electron_shellnist-atomic-states