Quantum mechanics early developments leading

This experimental development was matched by rapid theoretical progress, and the comparison and interplay between theory and experiment has been important in the field of metrology, leading to higher precision in the determination of the fundamental constants. We feel that now is a good time to review modern bound state theory. The theory of hydrogenic bound states is widely described in the literature. The basics of nonrelativistic theory are contained in any textbook on quantum mechanics, and the relativistic Dirac equation and the Lamb shift are discussed in any textbook on quantum electrodynamics and quantum field theory. An excellent source for the early results is the classic book by Bethe and Salpeter [6]. A number of excellent reviews contain more recent theoretical results, and a representative, but far from exhaustive, list of these reviews includes [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. 

All of these early studies, however, contained, in addition to suggestions that have since been incorporated into the present theory, many others that have been discarded. The refinement of the electronic theory of valence into its present form has been due almost entirely to the development of the theory of quantum mechanics, which has not only provided a method for the calculation of the properties of simple molecules, leading to the complete elucidation of the phenomena involved in the formation of a covalent bond between two atoms and dispersing the veil of mystery that had shrouded the bond during the decades since its existence was first assumed, but has also introduced into chemical theory a new concept, that of resonance, which, if not entirely unanticipated in its applications to chemistry, nevertheless had not before been clearly recognized and understood. 

Physical chemistry is known for its heavy use of mathematics, which can makes the subject seem abstract. Therefore, it is no surprise that mathematics ability has been found to be a good predictor of student success in physical chemistry (House 1995 Bers 1997 Nicoll and Francisco 2001). The emphasis on mathematics, combined with a traditional focus on the early development of thermodynamics and quantum mechanics, leads to the impression that physical chemistry is a theoretical science, with only tenuous connections to real science. However, making connections to concepts or applications that are known to or relevant to students can be difficult or impossible if attempted through a hands-on approach. Equipment costs and availability, time limitations, and expertise can all hinder such efforts. There again, a technology-based approach can provide a solution. 

The mathematics taught to researchers in science is almost exclusively focused on the Hilbert theory of infinite matrices an object such as a continued fraction may thus be unfamiliar to them. Historically mathematical discoveries have followed a different pattern. The analytic theory of continued fractions of Stieltjes inspired and preceded by almost a decade the pioneering work of Hilbert and his school. The development of quantum mechanics in the early part of this century has granted to the latter a leading role. ... 

The American quantum chemistry community developed very quickly. As Dresden (1992) pointed out, this could be due to the fact that many of the founders of American quantum chemistry had a very similar development, leading from an early exposure to preliminary quantmn theory via a substantial apprenticeship in formal quantum mechanics to a notable success in atomic and molecular structure (page 28). This common path of development helped enormously to create a well-trained, coherent quantmn chemistry community in the USA. 

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