## Abstract

Investigations on the nature of light showed that, depending on the kind of experiment performed, light must be described by electromagnetic *waves* or by *particles* (photons). Thus the wave aspect appears in the context of diffraction and interference phenomena, whereas the particulate aspect shows up most distinctly in the photoelectric effect. So for light, the relations describing wave-particle duality are already known. But what about material particles? Their particulate nature is rather obvious; do they also possess a wave aspect?

### Keywords

Permeability Manifold Sine Tate Azimuth## Preview

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### Biographical Notes

**de Broglie**, Prince Louis Victor, French physicist, 1892–1987, professor of theoretical physics at the Institut Henri Poincaré. He founded with his Ph.D. thesis “Recherches sur la Théorie des Quants” (1924) the*theory of matter waves (de Broglie waves)*and was awarded the Nobel Prize in Physics for it in 1929. Later he worked mainly on the development of the quantum theory of elementary particles (neutrino theory of light, wave theory of elementary particles) and proposed a new method for the treatment of wave equations with higher spin, the so-called*fusion method*. Google Scholar**Davisson**, Clinton Joseph, American physicist, * Bloomington (IL), 22.10.1881, † Charlottesville (VA), 1.2.1958. From 1917 to 1946 D. was a scientist at Bell Telephone Laboratories; then, until 1954, he was a professor at the University of Virginia in Charlottesville. In 1927 D. and L.H. Germer measured electron diffraction by crystals, a decisive proof of the wave nature of matter. In 1937 he was awarded the Nobel Prize in Physics.Google Scholar**Laue**, Max von, German physicist, * Pfaffendorf (near Koblenz, Germany), 9.10.1879, † Berlin, 24.4.1960. v.L. was a student of M. Planck, a professor in Zurich, Frankfurt, Berlin and, from 1946, Director of the Institut für Physikalische Chemie und Elektrochemie in Berlin-Dahlem. v.L. was the first director of the Institut für Theoretische Physik in Frankfurt (from 1914 until 1919), his successor being M. Born. His proposal to irradiate crystals with X-rays was performed by Walther Friedrich and Paul Knipping in late April 1912. L.’s immediate explanation of the X-ray interferences detected in this experiment won him the Nobel Prize in Physics in 1914. With this, the wave nature of X-rays as well as the spatial grating structure of crystals was established. As early as 1911, v.L. wrote a book about the theory of relativity, which was widely read, and in which he later included general relativity. He also worked on the applications of relativity, e.g. on thermodynamics. Further treatises covered superconductivity, glow-electron emission and the mechanism of amplifier valves. After 1933 v.L. tried, often successfully, to oppose the influence of national socialism on science in Germany.Google Scholar**Born**, Max, German physicist, * Breslau, Germany (now Wroclaw, Poland) 12.12.1882, † Göttingen 5.1.1970. B. was a professor in Berlin (1915), Frankfurt (1919) and Göttingen (1921); he emigrated to Cambridge in 1933 and then became Tait Professor of Natural Philosophy in Edinburgh in 1936. From 1954 on, B. lived in retirement in Bad Pyrmont (Germany). B. first devoted himself to relativity and the physics of crystals. From about 1922 on, he worked on the foundation of a new theory of atoms and succeeded in 1925, together with his students W. Heisenberg and P. Jordan, in the creation of matrix mechanics. In Göttingen, B. founded an important school of theoretical physics. In 1926 he interpreted Schrödinger’s wave functions as probability amplitudes, thus introducing the statistical point of view into modern physics. For this he was belatedly awarded the Nobel Prize in 1954.Google Scholar**Hilbert**, David, * Königsberg, Germany (now USSR) 23.1.1862, † Göttingen 14.2.1943. H., son of a lawyer, studied in Königsberg and Heidelberg and became a professor in Königsberg in 1886. From 1895 on, he contributed to making Göttingen a world centre of mathematical research. The most important living mathematican, H. proved himself as a world-wide authority in his famous talk given in Paris in 1900, where he proposed 23 mathematical problems which interest mathematicians even today. H. contributed to many fields that have deeply influenced modern mathematical research, e.g. on the theory of invariants, group theory and the theory of algebraic manifolds. His investigations on number theory culminated in 1897 in his report, “Die Theorie der algebraischen Zahlkörper” and in his proof of War-ring’s Problem. In the field of geometry he introduced strictly axiomatic concepts in “Die Grundlagen der Geometrie” (1899). His works on the theory of integral equations and on the calculus of variations strongly influenced modern analysis. H. also worked successfully on problems of theoretical physics, especially on kinetic gas theory and relativity. As a consequence of the development of set theory and the problems arising in the foundations of mathematics, H. created his proof theory and thereby became one of the leaders of the axiomatic branch of the foundation of mathematics.Google Scholar**Heisenberg**, Werner Karl, German physicist, * Würzburg 5.12.1901, † München 1.2.1976. From 1927–41 he was Professor of Theoretical Physics in Leipzig and Berlin; in 1941, professor at, and director of, the Max-Planck-Institute für Physik in Berlin, Göttingen and, from 1955 on, in München. In his search for the correct description of atomic phenomena, H. formulated his*positivistic principle*in July of 1925: it asserts that only quantities which are in principle observable are allowed to be taken into account. Thus the more intuitive ideas of the older Bohr-Sommerfeld quantum theory have to be rejected. At the same time H. provided the foundation for the new Göttinger matrix mechanics in his rules for multiplication of quadratic schemata, which he developed together with M. Born and P. Jordan in Sept. of 1925. In close collaboration with N. Bohr he was able to show the deeper physical or philosophical — background of the new formalism. The Heisenberg uncertainty principle of 1927 became the basis of the*Copenhagen interpretation*of quantum theory. In 1932 H. was awarded the Nobel Prize in Physics “for the Creation of Quantum Mechanics”. After the discovery of the neutron by J. Chadwick in 1932, H. realized that this new particle together with the proton must be considered as constituents of atomic nuclei. On this basis he developed a theory of the structure of atomic nuclei and introduced, in particular, the concept of isospin. From 1953 on, H. worked on a unifying theory of matter (often called a*world formula)*. The aim of this theory is to describe all existing particles and their conversion processes using the conservation laws, which express the symmetry properties of the laws of nature. A nonlinear spinor equation is supposed to describe all elementary particles.Google Scholar**Jacobi**, Carl Gustav Jakob, * 10.12.1804 in Potsdam as the son of a banker, † 18.2.1851 in Berlin. J. became an instructor in Berlin after his studies in 1824 and 1827/42 was professor in Königsberg (Prussia). After an extended travel to Italy, which was to cure his impaired health. J. lived in Berlin as a university man. He became famous because of his work “Fundamenta nova theoriae functiorum ellipticarum” (1829). In 1832, J. found out that hyperelliptic functions can be inverted by functions of several variables. J. also made fundamental contributions to algebra, to elimination theory, and to the theory of partial differential equations, e.g. in his “Vorlesungen über Dynamik”, which were published in 1866.Google Scholar

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