Quantum mechanics of atoms

In the quantum mechanics of atoms and molecules, both perturbation theory and the variational principle are widely used. For some problems, one of the two classes of approach is clearly best suited to the task, and is thus an established choice. Flowever, in many others, the situation is less clear cut, and calculations can be done with either of the methods or a combination of both. 

The miderstanding of the quantum mechanics of atoms was pioneered by Bohr, in his theory of the hydrogen atom. This combined the classical ideas on planetary motion—applicable to the atom because of the fomial similarity of tlie gravitational potential to tlie Coulomb potential between an electron and nucleus—with the quantum ideas that had recently been introduced by Planck and Einstein. This led eventually to the fomial theory of quaiitum mechanics, first discovered by Heisenberg, and most conveniently expressed by Schrodinger in the wave equation that bears his name. 

E. P. Wigner, Group Theory and Its Applications to the Quantum Mechanics of Atomic Spectra, Academic Press, New York, 1959. 

I tried to consistently distinguish between the quantum mechanics of atomic and molecular properties on the one hand and quantum collision theory on the other. The present discussion follows the same pattern. 

W. Thirring, Quantum Mechanics of Atoms and Molecules, Springer, New York, 1981. 

But chaos is more than a tool. There are as yet unsolved philosophical problems in its wake. While relativity and quantum mechanics necessitated - and in fact originated from - a careful analysis of the concepts of space, time and measurement, chaos, already on the classical level, forces us to re-think the concepts of determinism and predictability. Thus, classical mechanics could not be further removed from the dusty subject it is usually portrayed as. On the contrary it is at the forefront of modern scientific research. Since path integrals provide a link between classical and quantum mechanics, conceptual and philosophical problems with classical mechanics are bound to manifest themselves on the quantum level. We are only at the beginning of a thorough exploration of these questions. But one fact is established already chaos has a profound in-fiuence on the quantum mechanics of atoms and molecules. This book presents some of the most prominent examples. 

Wigner, E. P. Group theory and its application to the quantum mechanics of atomic spectra. New York Academic Press 1959. 

Y. S. Kim and M. E. Noz, Theory and Applications of the Poincare Group Reidel, 1986. One of the pioneering books on group theory that clearly explicates the spinor role in relativistic covariance is E. P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, Academic, New York, 1959. 

Niels Bohr, who was awarded the 1922 Nobel Prize in physics for his work in the quantum mechanics of atomic structure, shown here with his mother (Niels Bohr Archive, courtesy AIP Emilio Segre Archives)... 

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