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volume II: Synopsis

part III: Modern Physics

page 18: Quantum mechanics

Quantum mechanics began with the work of Max Planck at the turn of the twentieth century. It took nearly thirty years to reach its modern form, largely because the ideas it introduced into physics were very new and strange. The development of quantum mechanics was driven by a growing list of inconsistencies observed between Newtonian physics and observations of the microscopic world of atoms, electrons, photons and other particles. Quantum mechanics - Wikipedia

The historical roots of quantum mechanics lie in the relationship between matter and radiation. Hot matter emits electromagnetic radiation. In 1859 Kirchoff used a thermodynamic argument to show that the rate of emission of radiation from a body was a function of the temperature of the body and the frequency of the radiation only. He wrote 'it is a highly important task to find this function'. Gustav Kirchoff - Wikipedia

Max Planck found that function in 1900, but to provide a plausible derivation of it, he had to make an 'act of desperation': he assumed that the exchange of energy between material oscillators and the electromagnetic field was constrained by the relationship E = hf, where E is the energy, f the frequency of the radiation, and h a universal constant (Planck's constant). Pais page 372. Planck's discovery came amidst a growing body of experimental data that seemed impossible to explain using Newtonian physics. Planck's Law - Wikipedia

Of particular interest were the spectra of atoms. Systematic measurement of atomic spectra had begun in the middle of the nineteenth century, and by the end of the century spectroscopists, as measurers of spectra are called, were making measurements of very high precision.

Each atom can radiate and absorb across a spectrum of 'spectral lines'. Each spectral line has a fixed measurable frequency that seems to be determined by nature to unlimited precision. Classical physics could not explain this. The first quantum explanation was due to Niels Bohr, who found that he could explain the Rydberg-Ritz combination principle by assuming that the electronic orbits in the hydrogen atom were separated by one quantum of angular momentum. Rydberg-Ritz combination principle - Wikipedia, History of quantum mechanics - Wikipedia, Niels Bohr - Wikipedia

Bohr's model worked well for hydrogen but would not work for more complex atoms. The final answer came in two forms. In 1925 Werner Heisenberg published his first paper on 'matrix mechanics'. In 1926 Erwin Schrödinger published the Schrödinger (energy) equation, laying the foundation of 'wave mechanics'. Both took account of the interactions between all the electronic orbits in an atom, an approach found necessary to model the energy of the atomic spectral lines correctly. Werner Heisenberg - Wikipedia, Schrödinger equation - Wikipedia

Both approaches to quantum mechanics were soon shown to be mathematically equivalent. This demonstration, took advantage of the mathematical theory of function spaces. This theory has been developed by David Hilbert, among others, and took advantage of Cantor's invention of set theory and of transfinite numbers. As in the case of Newton and calculus, it took a major advance in mathematics to produce a system powerful enough to model the complexity of the physical Universe. David Hilbert - Wikipedia

[revised 23 May 2013]

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Further reading

Books

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Brandt, Siegmund, and Hans Dieter Dahmen, The Picture Book of Quantum Mechanics, Springer-Verlag 1995 Jacket: 'This book is an introduction to the basic concepts and phenomena of quantum mechanics. Computer-generated illustrations are used extensively throughout the text, helping to establish the relation between quantum mechanics on one side and classical physics ... on the other side. Even more by studying the pictures in parallel with the text, readers develop an intuition for notoriously abstract quantum phenomena ...' 
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Davies, Paul C W, and David S Betts, Quantum Mechanics, Chapman and Hall 1994-1995 Jacket: 'Quantum mechanics is the key to modern physics and chemistry, yet it is notoriously difficult to understand. This book is designed to overcome that obstacle. Clear and concise, it provides an easily readable introduction intended for science undergraduates with no previous knowledge of quantum theory, leading them through to the advanced topics usually encountered at the final year level. Although the subject matter is standard, novel techniques have been employed that considerably simplify the technical presentation. The authors use their extensive experience of teaching and popularizing science to explain the many difficult, abstract points of the subject in easily comprehensible language. Helpful examples and thorough sets of exercises are also given to enable students to master the subject.. 
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Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. ... In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands 
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Heilbron, J L, Dilemmas of an Upright Man: Max Planck and the Fortunes of German Science, Harvard University Press 2000 Winner of the History of Science Society's Watson Davis Prize for the Public Understanding of Science. In this moving and eloquent portrait, John Heilbron describes how the founder of quantum theory rose to the pinnacle of German science. With great understanding, he shows how Max Planck suffered morally and intellectually as his lifelong habit of service to his country and to physics was confronted by the realities of World War I and the brutalities of the Third Reich. In an afterword written for this edition, Heilbron weighs the recurring questions among painful choices Planck faced in attempting to build an "ark" to carry science and scientists through the storms of Nazism. 
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Kuhn, Thomas S, Black-Body Theory and the Quantum Discontinuity 1894-1912, University of Chicago Press 1987 Jacket: '[This book] traces the emergence of discontinuous physics during the early years of this century. Breaking with historiographic tradition, Kuhn maintains that, though clearly due to Max Planck, the concept of discontinuous energy change does not originate in his work. Instead it was introduced by physicists trying to understand the success of his brilliant new theory of black-body radiation.' 
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Lo, Hoi-Kwong, and Tim Spiller, Sandra Popescu, Introduction to Quantum Computation and Information, World Scientific 1998 Jacket: 'This book provides a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault tolerant quantum computation, as well as some experimental aspects of quantum computation and quantum cryptography. A knowledge of basic quantum mechanics is assumed.' 
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Pais, Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this ... major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. ... Running through the book is a completely non-scientific biography ... including many letters which appear in English for the first time, as well as other information not published before.' 
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Links
David Hilbert - Wikipedia David Hilbert - Wikipedia, the free encyclopedia 'David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He invented or developed a broad range of fundamental ideas, in invariant theory, the axiomatization of geometry, and with the notion of Hilbert space, one of the foundations of functional analysis. Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century. Hilbert and his students supplied significant portions of the mathematical infrastructure required for quantum mechanics and general relativity. He is also known as one of the founders of proof theory, mathematical logic and the distinction between mathematics and metamathematics.' back
Gustav Kirchoff - Wikipedia Gustav Kirchoff - Wikipedia, the free enclcylopedia Gustav Robert Kirchhoff (12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coined the term "black body" radiation in 1862, and two sets of independent concepts in both circuit theory and thermal emission are named "Kirchhoff's laws" after him. The Bunsen-Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen back
History of quantum mechanics - Wikipedia History of quantum mechanics - Wikipedia, the free encyclopedia 'The history of quantum mechanics, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859-1860 winter statement of the black body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements". . . ' back
Niels Bohr - Wikipedia Niels Bohr - Wikipedia, the free encyclopedia 'Niels Henrik David Bohr (Danish pronunciation: [nels ˈb̥oɐ̯ˀ]; 7 October 1885 – 18 November 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, . . . Bohr has been described as one of the most influential physicists of the 20th century' back
Planck's Law - Wikipedia Planck's Law - Wikipedia, the free encyclopedia 'In physics, Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at temperature T. As a function of frequency nu. back
Quantum mechanics - Wikipedia Quantum mechanics - Wikipedia, the free encyclopedia 'Quantum mechanics, also known as quantum physics or quantum theory, is a theory of physics providing a mathematical description of the interaction of matter and energy.' back
Rydberg-Ritz combination principle - Wikipedia Rydberg-Ritz combination principle - Wikipedia, the free encyclopedia 'The Rydberg-Ritz Combination Principle is the theory proposed by Walter Ritz in 1908 to explain relationship of the spectral lines for all atoms. The principle states that the spectral lines of any element include frequencies that are either the sum or the difference of the frequencies of two other lines.' back
Schrödinger equation - Wikipedia Schrödinger equation - Wikipedia, the free encyclopedia 'In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1926, describes the space- and time-dependence of quantum mechanical systems. It is of central importance in non-relativistic quantum mechanics, playing a role for microscopic particles analogous to Newton's second law in classical mechanics for macroscopic particles. Microscopic particles include elementary particles, such as electrons, as well as systems of particles, such as atomic nuclei.' back
Werner Heisenberg - Wikipedia Werner Heisenberg - Wikipedia, the free encyclopedia 'Werner Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist, best known for asserting the uncertainty principle of quantum theory. He made important contributions to quantum mechanics, nuclear physics, quantum field theory, and particle physics.' back

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