Mechanics and the Old Quantum Theory

The molecular nature of matter is studied through quantum mechanics. 

Classical mechanics is the historical precursor of quantum mechanics. 

In this theory the state of a system is specihed hy giving values of coordinates and velocities. 

Classical mechanics accurately describes the motions of objects of large mass that are moving at speeds much slower than the speed of light. 

Classical mechanics ascribes exact trajectories to particles. 

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These results were true for classical mechanics and the old quantum theory, and had been assumed without proof by many people before the work of Born and Oppenheimer was published. 

In the period between 1926 and 1939 the development of our understanding of radiation processes parallels the development of the theory of atomic and molecular structure. Many of the results which had been derived by the use of the correspondence principle and the old quantum theory were re-derived in a more rigorous and satisfactory manner. The quantum-mechanical expression for the refractive index of a gas or vapour is an example of this type of progress. In hydrogenic systems the rates of radiative transitions were calculated and the theoretical lifetimes of the different excited levels were derived. In other atoms only approximate estimates of the transition probabilities were possible, but the lifetime measurements made by canal rays and fluorescence from atomic beams were not sufficiently accurate to demand more refined calculations. 

This is a crudal and frequently overlooked point about electronic configurations. They are far from being based in quantum mechanics it is precisely this theory that shows them to be an inadequate concept The notion that electron orbits and configurations really exist or "refer" is a relic of the old quantum theory and of Pauli s introduction of the exclusion prind-ple in its original and now strictly incorrect... 

Only with Bohr s 1913-1923 introduction of the "old quantum theory" (itself strongly inspired by chemical periodicity patterns vide infra) and the final discovery of Schrodinger s wave mechanics in 1925 would the periodic table be supplanted as the deepest expression of current chemical understanding ([21], p 2). 

In recent years the old quantum theory, associated principally with the names of Bohr and Sommerfeld, encountered a large number of difficulties, all of which vanished before the new quantum mechanics of Heisenberg. Because of its abstruse and difficultly interpretable mathematical foundation, Heisenberg s quantum mechanics cannot be easily applied to the relatively complicated problems of the structures and properties of many-electron atoms and of molecules in particular is this true for chemical problems, which usually do not permit simple dynamical formulation in terms of nuclei and electrons, but instead require to be treated with the aid of atomic and molecular models. Accordingly, it is especially gratifying that Schrodinger s interpretation of his wave mechanics3 provides a simple and satisfactory atomic model, more closely related to the chemist s atom than to that of the old quantum theory. 

This equation, including succeeding terms, was obtained originally by Sommerfeld from relativistic considerations with the old quantum theory the first term, except for the screening constant sQ> has now been derived by Heisenberg and Jordan] with the use of the quantum mechanics and the idea of the spinning electron. The value of the screening constant is known for a number of doublets, and it is found empirically not to vary with Z. 

Discussing physics with Bohr was sometimes quite exhausting. In 1925, while working at Bohr s institute, Heisenberg discovered quantum mechanics, the theory that superseded the old quantum theory that had been developed by Bohr and his colleagues. Then, in 1926, a theory that looked much different from Heisenberg s, but which turned out to be mathematically equivalent, was propounded by the Austrian physicist Erwin Schrodinger. 

Quantum mechanics, which replaced the old quantum theory, was not easy to interpret. It conceived of both light and particles as having a dual nature. They were sometimes observed to be waves and sometimes particles, depending on the type of experiment that one performed. For example, the electron seemed sometimes to be a particle and sometimes a packet of waves. Furthermore, quantum mechanics described the subatomic world in terms of probabilities. 

Ttuming now to the electronic interaction, the analysis of Himd provides the important result that the electronic term of the lowest state of a molecule changes continuously from its value for a neutral atom of equal number of electrons to its value for the dissociated atoms, according to the new quantum mechanics. Herein lies an important difference between the old and the new quantum theory which is essential to the argument of this paper. That imexcited molecules dissociate into two unexcited... 

Atomic. From spectroscopic studies, it is known lliat when an electron is bound to a positively charged nucleus only certain fixed energy levels are accessible to the electron. Before 1926, the old quantum theory considered that the motion of the electrons could be described by classical Newtonian mechanics in which the electrons move in well defined circular or elliptical orbits around the nucleus. However, the theory encountered numerous difficulties and in many instances there arose serious discrepancies between its predictions and experimental fact. 

A reactionary movement started with the work of Leopold and Per-cival (1980). Using modern semiclassical techniques these authors were able to show that the old quantum mechanics was not so bad after all. Improving the old theory with the help of Maslov indices and variational techniques, Leopold and Percival showed that the old quantum theory yields results for the ground state and excited states of helium that are within the experimental accuracy achieved by the 1920s. Thus, Leopold and Percival turned the failure of the old quantum theory into a success, since the accuracy of the semiclassical theory improves with increasing quantum numbers and turns out to be a very useful tool for the computation of highly excited states. 

Perhaps this is too easy. Perhaps the importance of the duty of universal applicability is as a motivation, rather than as an achievement attempts to unify disparate domains have motivated some of the most ambitious and successful episodes in the history of physics. Newtonian mechanics, we are often told, was the synthesis of terrestrial and astronomical physics. More poignantly for the present discussion, in the early 1920s—the last years of the old quantum theory—attempts to fit atomic models to spectroscopic data required a diverse battery of inexplicable and mutually incompatible quantum conditions. Pauli and Bom, among others, saw in this chaos the need for a radical departure. Hindsight tells us that it was quantum mechanics... 

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