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The Quantization of Physical Quantities

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Quantum Mechanics
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Abstract

In order to explain physical phenomena caused by light, two points of view have emerged, each of which has its place in the history of physics. Almost simultaneously in the second half of the seventeenth century the corpuscle theory was developed by Newton and the wave theory of light was created by Huygens. Some basic properties like the rectilinear propagation and reflection of light can be explained by both theories, but other phenomena, such as interference, the fact that light plus light may cause darkness, can be explained only by the wave theory.

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Biographical Notes

  • Hertz, Heinrich Rudolf, German physicist, *Hamburg 22.2.1857, †Bonn 1.1.1894, a professor of physics in Karlsruhe and Bonn, confirmed with his experiments concerning the propagation of electromagnetic waves the predictions of Maxwell’s electromagnetic theory of light in 1887/88. He discovered the so-called Hertz waves, which are the physical fundamentals of modern radio engineering. He proved the influence of ultraviolet light on electrical discharge (1887), which led to the discovery of the photoelectric effect by W. Hallwachs. In 1892 H. observed the transmission of cathode rays through thin metal plates and gave P. Lenard the task of explaining their nature. H. also gave an exact definition of hardness.

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  • Lenard, Philipp, German physicist, * Preßburg 7.6.1862, † Messelhausen (Baden-Württ.) 20.5.1947, student of H. Hertz, was a professor in Breslau, Aachen, Kiel and Heidelberg. Using the window tube suggested by Hertz, L. was the first to investigate cathode rays as free electrons independent of the way they were generated and made a major contribution to the explanation of the nature of these rays. Among other things he showed that the rate of absorption of cathode rays is nearly proportional to the mass of the radiated substance. Furthermore he demonstrated that the velocity of electrons emitted due to the photoelectric effect is independent of the intensity of light, but depends on its frequency. Thus he created the experimental foundation for the fundamental photoelectric law formulated by Einstein. Of equal importance was his verification that the active centre of an atom is concentrated in a nucleus, which is tiny in comparison with the radial dimension of the whole atom. Later this fact was also experimentally proved by E. Rutherford. The explanation of the mechanism of phosphorescence and the proof that an electron must have a definite minimum energy to ionize an atom are further achievements by L. He also introduced the “electron-volt” (eV) as a unit of measurement. In 1905 he received the Nobel Prize in Physics. L. was as renowned an experimental physicist as his contemporaries J.J. Thomson and E. Rutherford, but was sceptical of Einstein’s Special Theory of Relativity. He rejected the Weimar Republic and gradually developed into a fanatical anti-semite and national socialist. [BR]

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  • Einstein, Albert, German physicist, *Ulm 31.4.1879, †Princeton (N.J.) 18.4.1955. Having grown up in Munich, he moved to Switzerland at the age of 15. As a “technical expert third class” at the patent office in Bern, he published in 1905 in Vol. 17 of An-nalen der Physik three most important papers. In his “On the theory of Brownian motion” he published a direct and conclusive proof, based on a purely classical picture, of the atomistic structure of matter. In his paper, “On the electrodynamics of moving bodies”, he set up with his profound analysis of the terms “space” and “time” the Special Theory of Relativity. Prom this he concluded a few months later the general equivalence of mass and energy, expressed by the famous formula E = mc 2. In his third article, E. extended the quantum approach of M. Planck (1900) in “On a heuristic viewpoint concerning the production and transformation of light” and made the second decisive step towards the development of quantum theory, directly leading to the idea of the duality of particles and waves. The concept of light quanta was considered too radical by most physicists and was very sceptically received. A change in the opinion of physicists did not take place until Niels Bohr proposed his theory of atoms (1913). E., who became a professor at the University of Zürich in 1909, went to Prague in 1911, and returned to Zürich a year later where he joined the Eidgenössische Technische Hochschule. In 1913 he was called to Berlin as a full-time member of the Preussische Akademie der Wissenschaften and director of the Kaiser-Wilhelm-Institut für Physik. In 1914/15 he developed the General Theory of Relativity, starting from the strict proportionality of gravitational and inertial mass. As a result of the successful testing of his theory by a British solar eclipse expedition, E. became well known to the general public. His political and scientific opponents tried unsuccessfully to start a campaign against him and his theory of relativity. The Nobel Prize Committee therefore considered it advisable to award E. the 1921 Nobel Prize in Physics not for his theory of relativity, but for his contributions to quantum theory. Beginning in 1921 E. tried to set up his unified theory of matter which aimed to incorporate electrodynamics as well as gravitation. Even after it had been shown by H. Yukawa that other forces exist besides gravitation and electrodynamics, he continued with his efforts which, however, remained unsuccessful. Although he published a paper in 1917 which was instrumental to the statistical interpretation of quantum theory, he later raised severe objections, based on his philosophical point of view to the “Copenhagen Interpretation” proposed by N. Bohr and W. Heisenber. Several attacks because of his Jewish background caused E. in 1933 to relinguish all the academic positions he held in Germany; at the Institute for Advanced Study in Princeton, in the U.S.A., he found somewhere new to continue his studies. The final stage of E.’s life was overshadowed by the fact that although a life-long pacifist, fearing German aggression he initiated the development of the American atomic bomb by writing, together with others, to President Roosevelt on 8.2.1939. [BR]

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  • Compton, Arthur Holly, American physicist, * Wooster (Ohio) 10.9.1892, †Berkeley (CA) 15.3.1962, became a professor at Washington University, St. Louis, in 1920 and at the University of Chicago in 1923. In 1945 he became chancellor of Washington University. In the course of his investigations on X-rays he discovered the Compton effect in 1922. He and Debye simultaneously gave the quantum-theoretical explanation for this effect. C. was also the first to prove the total reflection of X-rays. Together with R.L. Doan, he achieved the diffraction of X-rays from a diffraction grating. Jointly with C.T.R. Wilson he was awarded the Nobel Prize in Physics in 1927. In cooperation with his students C. carried out extensive investigations on cosmic rays. During the Second World War he participated in the development of the atomic bomb and radar as director of the plutonium research project of the American Government. [BR]

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  • Debye, Petrus Josephus Wilhelmus, Dutch physicist, naturalized in America in 1946, * Maastricht (Netherlands) 24.3.1884, †Ithaca (N.J.) 2.11.1966, was called “the Master of the Molecule”. In 1911 he became a professor at the University of Zürich as successor to A. Einstein, then in Utrecht (1912–1914), Göttingen (1914–1920), at the Eidgenössische Technische Hochschule in Zürich (1920–1927), in Leipzig (1927–1935), and was director of the Kaiser-Wilhelm-Institut für Physik in Berlin, 1935–1939. In 1940 he emigrated to the United States and became a professor of chemistry at Cornell University (Ithaca) in 1948. There he directed the chemistry department from 1940 until his retirement in 1952. D. was famous both as a theoretical and as an experimental physicist. He formulated the T3 law for the decrease of the specific heat of solids at low temperatures. He developed the Debye-Scherrer method (1917 independently of A.W. Hull) and, jointly with E. Hückel, formulated a theory of dissociation and conductivity of strong electrolytes. Independently of F.W. Glau-gue and almost at the same time D. pointed out the possibility of reaching low temperatures by adiabatic demagnetization of ferromagnetic substances. During extensive research, he determined the dipole moments of molecules. This research together with results of the diffraction experiments of X-rays and electron rays from gases and liquids enabled him to establish their molecular structure; for this he was awarded the Nobel Prize in Chemistry in 1936. After his retirement, he developed methods to determine the molecular weight and the molecular expansion of giant molecules of highly polymerized sustances. [BR]

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  • Ritz, Walter, Swiss physicist, * Sitten 22.2.1878, †Göttingen 7.7.1909, formulated the combination principle for spectral lines in 1908.

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  • Franck, James, German physicist, * Hamburg 20.8.1882, †Göttingen (during a journey through Germany) 21.5.1964. Franck was a member of the Kaiser-Wilhelm-Institut für Physikalische Chemie, and, beginning in 1920, a professor in Göttingen; he left Germany in 1933. From 1935, F. was a professor of physics at John Hopkins University in Baltimore; 1938–1947, professor of physical chemistry in Chicago; from 1941 on, he was also active at the University of California. Jointly with G. Hertz, at the Physikalisches Institut in Berlin, F. investigated the energy transfer of electrons colliding with gas atoms. His results sustained Planck’s quantum hypothesis as well as the theory of spectral lines postulated by Bohr in 1913. For this work F. and Hertz were awarded the Nobel Prize in Physics in 1926. Extending these investigations, F. measured for the first time the dissociation energy of chemical compounds by optical means and determined the lifetime of met astable states of atoms. In addition he developed the law for the intensity distribution within a band structure, which is known today as the Franck-Condon principle. In the U.S.A. he devoted himself primarily to the investigation of photochemical processes within the living plant cell. During the Second World War F. worked on a project involving the technical utilization of nuclear energy. In 1945 he warned of the political and economic consequences of the use of atomic bombs in a petition which has become well known as the Frank Report. [BR]

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  • Hertz, Gustav, German physicist, nephew of Heinrich Hertz, * Hamburg 22.7.1887, first was a professor in Halle and Berlin and head of the research laboratory of the Siemens factories. From 1945–1954, H. built up an institute at Suchumi on the Black Sea together with former students and collaborators; in 1954 he directed a university institute in Leipzig. From 1911 on, together with J. Franck, he investigated the excitation of atoms by collisions with electrons; they shared the Nobel Prize in Physics in 1926. In 1932, H. developed the technique of isotope separation with a diffusion cascade consisting of many single steps. He applied this method to the extraction of uranium 235 on a large technical scale in the Soviet Union. [BR]

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  • Stern, Otto, German physicist, *Sorau (Niederlausitz) 17.2. 1888, †Berkeley (CA) 17.8.1969, became a professor in Rostock in 1921, and in Hamburg in 1923, where he also acted as director of the Physikalisch-Chemisches Institut. Beginning in 1915, S. developed the method of using molecular rays for the determination of atomic and nuclear properties. He had particular success in discovering the quantization of the magnetic moment (the Stern-Gerlach experiment), in his diffraction experiments with molecular hydrogen and helium rays (1929), and in determining the magnetic moment of the proton (begun in 1933). S. emigrated to the United States in 1933 and worked at the Carnegie Institute of Technology in Pittsburgh. In 1943, he was awarded the Nobel Prize in Physics. [BR]

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  • Gerlach, Walther, German physicist, * Biebrich a. Rh. 1.8.1889, †Munich 1979, professor in Frankfurt, Tübingen and from 1929 in Munich, determined the value of the Stefan-Boltzmann constant by precision measurements (1916). Together with Otto Stern he showed the quantization of the magnetic moment by deflection of atomic rays in an inhomogeneous magnetic field (1921). At that time G. was a lecturer at Physikalisches Institut der Universität Frankfurt a. M.; Otto Stern was visiting lecturer at the Institute für Theoretische Physik in Frankfurt, which was directed by Max Born (as successor to Max v. Laue) at that time. Furthermore, G. worked on quantitative spectral analysis and the coherence between atomic structure and magnetism. In extensive historical analyses of science, G. tried to point out the “humanistic value of physics”. [BR]

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© 1993 Springer-Verlag Berlin Heidelberg

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Greiner, W. (1993). The Quantization of Physical Quantities. In: Quantum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-30374-0_1

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  • DOI: https://doi.org/10.1007/978-3-662-30374-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56278-8

  • Online ISBN: 978-3-662-30374-0

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