VictoryTradiN 2. If you need a book that relates the core principles of quantum mechanics to modern applications in engineering, physics, and nanotechnology, this is it. Students will appreciate the book's applied emphasis, which illustrates theoretical concepts with examples of nanostructured materials, optics, and semiconductor devices. The many worked examples and more than homework problems help students to problem solve and to practise applications of theory. Without assuming a prior knowledge of high-level physics or classical mechanics, the text introduces Schroedinger's equation, operators, and approximation methods.
Systems, including the hydrogen atom and crystalline materials, are analyzed in detail. More advanced subjects, such as density matrices, quantum optics, and quantum information, are also covered. Hence, the solutions are:. For the final state, since the electron is not at rest, the equations are not so simple.
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As Yazaki shows, they solved this by introducing a contact transformation:. They define and by:. Then the Dirac equations take the same form as for :. In the case of the final state of the Compton effect, Klein and Nishina claim both and must be considered finite Klein and Nishina , Hence, it appears the wave functions for the final state have both components, namely:. In other words, for the final state of the electron, they combined or superposed the two independent solutions with variable phase factors.
Thus, behind the scenes, Nishina, with Klein, went back to his old friend from his electrical engineering student years—the principle of superposition—to carry out his first and most important work in quantum mechanics. For the value of , Klein and Nishina employed physical considerations and direct calculation. Hence the expectation value of , the magnetic moment of the electron, is zero.
The same value can be derived through straightforward calculation by plugging in the expression in eq. As for , one can get by inserting the expression in eq. Klein and Nishina did not clearly show how they justified this procedure for calculating a statistical average.
Summation over phases meant summation over the direction of the magnetic moment. At least for the initial state, the physical meaning was then clear. As for the final state, the situation was somewhat different, because the physical meanings of and were not transparent. They probably justified their assumptions by showing that vanishes by direct calculation.
Since they were considering unpolarized light as the incoming radiation, the average of the magnetic moment in the final state should also be zero. Since summation over phases eliminates non-diagonal elements and sums diagonal elements, this procedure can be considered equivalent to taking a trace. Because the density matrix in this case is proportional to the unit matrix, this procedure agrees with a quantum statistical calculation for a mixed state. A mathematical theory about this procedure of quantum statistics had already been presented by John von Neumann in , see von Neumann As I wrote at the beginning of this paper, I am not claiming any deterministic, causal connections.
It would be ridiculous to claim that Nishina worked on quantum mechanics because he studied electrical engineering. Nor do I claim that Nishina took a certain research style in quantum mechanics different from others because of his electrical engineering background. What I claim is that quantum mechanics, not only its experiments but also its theoretical research, might not be as disconnected from other fields of investigation, such as engineering, as we might assume. In terms of theoretical practices, there are some similarities between alternating current theory and quantum physics, at least in the way they were experienced by a person like Nishina.
At least in this limited sense, it seems the institutional and pedagogical developments in engineering helped introduce theoretical research in quantum mechanics into Japan.
ELEC 361(S): Quantum Mechanics for Engineers
Aichi, Keiichi Bartholomew, James R. Brown, Laurie M. Studies in History and Philosophy of Modern Physics Dalitz, Richard H. Another Side to Paul Dirac. Kursunoglu, Eugene P. Cambridge: Cambridge University Press Dirac, Paul A. Proceedings of the Royal Society A The Quantum Theory of the Electron. The Principles of Quantum Mechanics.
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Kim, Dong-Won Klein, Oskar, Yoshio Nishina Kline, Ronald R. Steinmetz: Engineer and Socialist. Baltimore: Johns Hopkins University Press. Kragh, Helge Dirac: A Scientific Biography. Cambridge: Cambridge University Press.
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Layton, Edwin Technology and Culture Denshiron The electron theory. Genkon no denkigaku Studies of electricity today. Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik. Nishina, Akira Memories of Dr. Nishina Yoshio. Takahashigawa Nishina, Yoshio Watashi wa nani o yondaka What I have read. Pyenson, Lewis Historical Studies in the Physical Sciences Bristol: Hilger.
Steinmetz, Charles Proteus Proceedings of the International Electrical Congress. Stuewer, Roger H.
New York: Science History Publications. Suchet, Charles Electrical Engineering Sugiura, Yoshikatsu Yagi, Eri Yazaki, Y. Kagakushi Kenkyu. Yukawa, Hideki On the Interaction of Elementary Particles I.. Proceedings of the Physico-Mathematical Society of Japan 17 3 : Following the common academic convention, I write Japanese names in the traditional order, the family name first, the given name second.
The drawing shows sine waves that resemble waves on the surface of water being reflected from two surfaces of a film of varying width, but that depiction of the wave nature of light is only a crude analogy. Early researchers differed in their explanations of the fundamental nature of what we now call electromagnetic radiation. Some maintained that light and other frequencies of electromagnetic radiation are composed of particles, while others asserted that electromagnetic radiation is a wave phenomenon. Ever since the early days of QM scientists have acknowledged that neither idea by itself can explain electromagnetic radiation.
For example, the behaviour of microscopic objects described in quantum mechanics is very different from our everyday experience, which may provoke some degree of incredulity. Dirac brought relativity theory to bear on quantum physics so that it could properly deal with events that occur at a substantial fraction of the speed of light.
Classical physics, however, also deals with mass attraction gravity , and no one has yet been able to bring gravity into a unified theory with the relativized quantum theory. Reference Terms. The term "quantum mechanics" was first coined by Max Born in It can be explained by a model that depicts it as a wave. In classical physics these ideas are mutually contradictory. Despite the success of quantum mechanics, it does have some controversial elements. Related Stories.