The development of elementary quantum theory (Q2400541)

This book describes how quantum mechanics arose and has been developed step by step thereby changing fundamental beliefs grown up in a pure mechanistic world. The Book is organized in 14 chapters, an appendix, author and subject indexes. Every chapter begins with an abstract and keywords. The first two short chapters outline the scope: from Planck's law until Copenhagen interpretation. The fundamental differences between classical and quantum physics are emphasized. Chapter 3 begins with M. Planck's motivation to seek for the radiation law and his success applying Boltzmann's statistics (1900). Einstein's explanation of the Photoelectric effect and conclusions thereof follow: quanta of light, quantization of atom oscillations in solids and specific heat, fluctuations of momentum and energy in the radiation field. Max Born and Werner Heisenberg's considerations to the quantum theory of radiation as well as, finally, the statistics of indistinguishable particles and the Bose-Einstein condensation are reported. Each research result is cited by the original publication. Chapter 4 considers the ``Old Quantum Theory,'' 1913--1924. That atoms or molecules emit only certain frequencies of light was observed in 1908 by Walter Ritz who denied the existence of Einstein's light quanta at that time. The discrete line spectra suggested Niels Bohr in 1813 to his famous postulates for the planetary model of atoms. Bohr's thoughts are displayed in a simple form. It is mentioned that the Compton effect gave some support for Einstein's light quanta hypothesis, but only four citations are given. The reason for the support, i. e. the consideration of single scattering processes of light quanta with particles, is omitted, probably because Niels Bohr and a majority of others did not accept this interpretation. Instead, the Bohr-Kramers-Slater (BKS) theory concerning interactions of light with matter is described as the final step of the old quantum theory. Chapter 5 begins with Max Born's proclamation that quantum mechanical micro-processes are basically discontinuous during the years 1919-1924. He considered Hamilton-Jacobi's action-angle variables to quantize the action resulting in quantum leaps. Born created the word ``quantum mechanics.'' Considering interactions of light with matter resulted in ``quantum optics.'' This development is described citing several papers and correspondences among physicists involved. Heisenberg's idea of matrix mechanics is understood as a reconciliation of proposals by Born and by Bohr. The result is formulated in the papers [\textit{M. Born} and \textit{P. Jordan}, Z. Phys. 34, 858--888 (1925; JFM 51.0728.08)], and [\textit{M. Born} et al., Z. Phys. 35, 557--615 (1926; JFM 52.0963.01)] considering matrices to represent physical quantities. Their commutation relations replace Poisson brackets. So, a quantum dynamics in a kind of Heisenberg picture arose in which only discontinuous state transitions happen. Heisenberg's visit in Cambridge brought Dirac to publish his conclusions in [\textit{P. A. M. Dirac}, Proc. R. Soc. Lond., Ser. A 109, 642--653 (1925; JFM 51.0729.01)]. Wolfgang Pauli successfully applied matrix mechanics to derive the hydrogen spectrum, angular momenta, the Stark effect were explained, and the Runge-Lenz vector was detected too. Differences in the understanding and proposals of Born-Jordan and Bohr-Heisenberg are reported. Pauli and Heisenberg came from Munich to Göttingen as doctors qualified by Sommerfeld to work with Born who was the supervisor of Jordan. Pauli's sceptical attitude towards Born influenced Heisenberg, and both, Pauli and Heisenberg, admired Niels Bohr. Heisenberg visited Copenhagen and his contacts with Bohr became much stronger than those with Born. A comparison of the methods of the old and the new quantum theory closes the chapter. Chapter 6 reports how the new quantum theory came back to continuous space and time. Kornel Lanczos was the first proposing that the properties of quantum systems may be expressed by integral or differential equations. Togethet with Norbert Wiener Born introduced Hermitian operators in inner product function spaces replacing Heisenberg's matrices in 1926. They found that the time dependence of an operator \(\mathrm{A}\) is given by \(e^{\frac{i}{\hbar}\mathrm{H}t}\mathrm{A}e^{-\frac{i}{\hbar}\mathrm{H}t}\). Inspired by this and de Broglie*s matter waves, recognizing that the Energy has to be half bounded, Schrödinger formulated the position representation including his dynamics. Schrödinger's reflections about the use of Hermitian operators to represent physical quantities, the Bose-Einstein statistics, and especially to propose the Schödinger equation instead the usual wave equation are explicitly described. Just 4 days after \textit{E. Schrödinger}'s 5th respective paper [Ann. der Phys. (4) 79, 734--756 (1926; JFM 52.0967.02)] \textit{M. Born} published [Z. Phys. 37, 863--867 (1926; JFM 52.0973.03)] considering electron scattering by atoms, and proposed the absolute square of the wave function to be the position probability. Chapter 7 considers consequences arising from applications of the new quantum settings. The method to determine the wavelength of electromagnetic radiation observing interferences emerging after reflection from a graded surface was now explained with Einstein's light quanta too. This verified the duality of particles and waves as well as Einstein's light quantization. The description of scattering processes lead to the momentum representation of wave mechanics. Then uncertainties arising in quantum mechanics are considered. After general remarks \textit{W. Heisenberg}'s arguments given in [Z. Phys. 43, 172--198 (1927; JFM 53.0853.05)] are analysed. The reasonings of \textit{E. H. Kennard} [Z. Phys. 44, 326--352 (1927; JFM 53.0853.02)] which is elaborated by H. P. Robertson is mentioned. The chapter closes with Bohr's duality properties, and his complementarity principle. Chapter 8 describes early opposition to the Copenhagen interpretation Bohr accepted the new developments of quantum mechanics and used them to build the view now known as the Copenhagen interpretation. Schrödinger and Einstein criticised strongly Bohr's complementarity principle which leads to logical contradictions. But Bohr used his principle for to discard their arguments. A big part of the Chapter is endowed to Einstein's understanding of quantum theory. It starts reporting a struggle of Einstein with Podolsky about formulations due to the latter in the EPR paper concerning the incompleteness of quantum theory. For Einstein the main reason is the statistical character of quantum theory but less the emergence of common assignments of complementary properties by one and the same state. Respective correspondences among several theoreticians including Schrödinger, Heisenberg, and Born are reported. Chapter 9 entitled ``Orthodox Portrayals of the Development of Quantum Mechanics'' recommends the books by Max Jammer, B. L. van der Waerden, Jagdish Mehra and Helmut Rechenbach describing the development from the beginning to the Copenhagen interpretation. Summaries of each of these books are given. It is remarked that the third one adds a very detailed account to the content of chapter 5 of the present book, conclusions which differ from those given there are explicitly mentioned. In chapter 10 later criticisms to the Copenhagen interpretation are described. It begins with \textit{Alfred Landé}'s paper ``Quantum Fact and Fiction'' [Am. J. Phys. 33. 123 (1925)]. The departure from the Galileian principle by denying the possibility to state facts of physical reality is a point of the critics. Herewith he is in accord with H. Margenau and K. Popper besides of A. Einstein and E. Schrödiner. \textit{Arthur Fine}'s book ``The shaky game, Einstein realism and the quantum theory'' from 1996 describes Einstein's view of the quantum problem, his criticism to the Copenhagen interpretation, and contains his struggle with Podolsky and the Bohr- Einstein debate as well is thoroughly reviewed. The book by \textit{Don Howard} from 1994 ``Niels Bohr and contemporary philosophy'' endowed to Bohr's view is reviewed. A more thorough review is given to the two parts of the book by \textit{Mara Beller} from 1999: ``Quantum Dialogue, the making of a revolution.'' The first one concerns mainly matrix mechanics and Heisenberg, the second one considers influences, critics or acceptance, of the established Copenhagen interpretation. The final review is on the book from 2011 ``Philosophical Rhetoric in early quantum mechanics 1925-1927'' by \textit{Alexeij Kojevnikov} who calls Bohr the winner of debates about the interpretation of quantum theoy. The ``General conclusions'' are a short overview of the steps on the way to quantum theory described in this book. The appendix consists in four short sections containing additional hints to understand scattering processes, diffraction phenomena of particles, position measurement and uncertainty, and remarks to field quantization. The language for to describe phenomena of classical physics is not sufficient for to describe quantum phenomena, hence new concepts and rules of conclusion are required. These to find out was the difficulty in the early development of quantum mechanics. The author reports the philosophy and background ideas of the founders which could not be always straightforward because of the lacking language. This book is suitable for to be understood by interested laymen, young students, and philosophers.