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.