In 1926, Erwin Schrödinger published an equation that described electrons not as tiny planets orbiting a nucleus, but as standing waves. This mathematical function defines the location and wave-like behavior of an electron within an atom. The resulting atomic orbital is an approximate solution to this equation for electrons bound by the electric field of the nucleus. Each orbital represents a specific energy state where an electron might exist. These states are often called eigenstates in formal quantum mechanical language. An actual electron exists in a superposition of these states, which acts like a weighted average with complex number weights. For instance, an electron could be in a pure eigenstate labeled (2, 1, 0) or a mixed state combining multiple possibilities. Eigenstates make it easier to deal with the math involved in describing these complex systems. When one considers also their spin component, scientists speak of atomic spin orbitals instead. A state is actually a function of the coordinates of all the electrons, so that their motion is correlated. This correlation is often approximated by an independent-particle model of products of single electron wave functions.
Historical Evolution Of Models
Hantaro Nagaoka published an orbit-based hypothesis for electron behavior as early as 1904. His Saturnian Model placed positive charge into a central core pulling electrons into circular orbits reminiscent of Saturn's rings. Few people took notice of Nagaoka's work at the time because classical charged objects cannot sustain orbital motion without losing energy due to electromagnetic radiation. J.J. Thomson discovered the electron in 1897 and theorized that multiple electrons revolve in orbit-like rings within a positively charged jelly-like substance. This plum pudding model was the most widely accepted explanation between 1897 and 1909. Ernest Rutherford discovered that the bulk of atomic mass was tightly condensed into a nucleus in 1909. In 1913, Niels Bohr proposed a new model where electrons orbited the nucleus with classical periods but were permitted only discrete values of angular momentum. The Bohr model fixed the problem of energy loss from radiation by declaring there was no state below this ground state. It explained the origin of spectral lines which had been known experimentally since the middle of the 19th century. De Broglie suggested the existence of electron matter waves in 1924, allowing a Bohr orbiting electron to be seen as orbiting in a circle at a multiple of its half-wavelength. This period was immediately superseded by the full three-dimensional wave mechanics of 1926.