Many-Electron Wavefunctions

Abstract

Although the old quantum theory of Niels Bohr had great success in the interpretation of the line spectra of the hydrogen atom, it did not provide an adequate framework for the interpretation of the complex spectra of the many-electron atoms and molecules. Nevertheless the old theory had many clever proponents, who with a series of particularly shrewd guesses nailed down the structure of the periodic table and the theory of line spectra some time before the new wave mechanics. Notable was the exclusion principle of Pauli, which included a fourth quantum number in addition to the three which are associated with the orbital motion of each electron [4.1]. This was the key to explaining why there are two electrons in an s shell, 6 in p shell, etc., and toward a correct theory of the building-up principle of the periodic table. Almost immediately thereafter, Uhlenbeck and Goudsmit [4.2] published their evidence that the fourth quantum number referred to the spin of the electron, a concept that helped clarify much of the subsequent thinking on the subject. Indeed so much was understood on the basis of the old theory alone, that it might even appear that the 1926 theories of Schrödinger and Heisenberg, far from solving old problems, only raised new difficulties. The reason is that it proved so awkward and difficult to introduce spin into the new quantum mechanics.