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The stationary states a particle can have in a given potential distribution. Since any such state has a constant energy, the particle's wave function Y must satisfy HY = EY for some E >= 0. Here H is the Hamiltonian operator; since it is linear, this becomes an eigenvector equation on the space of all states. Thus orbitals are just the energy eigenstates of the particle.

Of particular importance are atomic orbitals and molecular orbitals, the stationary states of electrons in atoms and molecules.