sommerfeld diffraction (19 Ergebnisse)

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Buch. Zustand: Neu. Neuware - 1 Introduction.- 1.1 About Physical Optics.- 1.2 The Electromagnetic Spectrum.- 1.3 Overview of the Following Chapters.- References.- Problems.- 2 Maxwell's Equations and Plane Wave Propagation.- 2.1 Introduction.- 2.2 Some Preliminaries.- 2.3 Monochromatic Plane Waves.- 2.4 Polychromatic Plane Waves.- 2.5 Propagation in Polarizing Optical Systems.- 2.6 Striated Media.- References.- Problems.- 3 Material Polarization and Dispersion.- 3.1 Introduction.- 3.2 Complexity in the Microscopic World.- 3.3 A Derivation of the Lorentz-Lorenz Relation.- 3.4 The Spring Model of Matter.- 3.5 Wave Propagation in Dispersive Media.- 3.6 Macroscopic Models of More Exotic Effects.- References.- Problems.- 4 Wave Propagation in Anisotropic Media.- 4.1 Introduction.- 4.2 Microscopic Basis for the Existence of an Index Tensor.- 4.3 Fresnel's and the Index Ellipsoids.- 4.4 The Normal Surface and the Ray Surface.- 4.5 Some Propagation Effects in Crystals.- 4.6 Some Polarization Devices.- References.- Problems.- 5 Geometrical Optics.- 5.1 Introduction.- 5.2 The WKB Approximation as it Relates to Geometrical Optics.- 5.3 The Eikonal Equation.- 5.4 Energy Flow and Radiometry.- 5.5 Paraxial Ray Optics.- 5.6 About Optical Instruments.- 5.7 Phase Space and Liouville's Theorem.- References.- Problems.- 6 Interferenee.- 6.1 Introduction.- 6.2 The Michelson Interferometer.- 6.3 Other Interferometers.- 6.4 The Fabry-Perot Interferometer.- 6.5 Young's Interferometer and Spatial Coherence.- 6.6 Hanbury-Brown and Twiss Interferometer.- References.- Problems.- 7 Diffraetion.- 7.1 Introduction.- 7.2 Green's Theorem and Scalar Diffraction.- 7.3 Rayleigh-Sommerfeld Theory.- 7.4 Van Cittert-Zemicke Theorem.- 7.5 Diffraction Gratings and Spectrometers.- References.- Problems.

8 offprints & 1 mimeograph. Original wrappers. From the collection of Abraham Pais. Very good. INVENTORY: 1. MOSHINSKY Borodiansky, Marcos (1921-2009). Forces Tensorielles Dependant de la Vitesse. Offprint from: Le Journal de Physique et le Radium, Tome 13, Novembre 1954, page 264. Signed by Pais. Moshinsky was a Mexican physicist of Ukrainian-Jewish origin whose work in the field of elementary particles won him the Prince of Asturias Prize for Scientific and Technical Investigation in 1988 and the UNESCO Science Prize in 1997. 2. MOSHINSKY Borodiansky, Marcos. Diffraction in Time. Offprint from: The Physical Review, Vol. 88, No. 3, pp. 625-631, November 1, 1952. Original turquoise printed wrappers. Signed by Pais. "In a previous note a dynamical description of resonance scattering was given, and transient terms appeared in the wave function describing the process. To understand the physical significance of these terms, the transient effects that appear when a shutter is opened are discussed in this paper. For a nonrelativistic beam of particles, the transient current has a close mathematical resemblance with the intensity of light in the Fresnel diffraction by a straight edge. This is the reason for calling the transient phenomena by the name of diffraction in time. The shutter problem is discussed for particles whose wave functions satisfy the Schrodinger equation, the ordinary wave equation, and the Klein-Gordon equation. Only for the Schrodinger time-dependent equation do the transient wave functions resemble the solutions that appear in Sommerfeld's theory of diffraction. The connection of transient phenomena with the time-energy uncertainty relation, and the interpretation of the transient current in a scattering process, are briefly discussed. The relativistic wave functions for the shutter problem may play an important role in the dynamical description of a relativistic scattering process." :: abstract. 3. MOSHINSKY Borodiansky, Marcos. Poles of the S Matrix for Resonance Reactions. Offprint from: The Physical Review, Vol. 91, No. 4, pp. 984-985, August 15, 1953. Signed by Pais. 4. MOSHINSKY Borodiansky, Marcos. Transformation Brackets for Harmonic Oscillator Functions. From: Nuclear Physics 13 (1959) 104-116; North Holland Publishing Co., Amsterdam. "We define the transformation brackets connecting the wave functions for two particles in an harmonic oscillator common potential with the wave functions given in terms of the relative and centre of mass coordinates of the two particles. With the help of these brackets we show that all matrix elements for the interaction potentials in nuclear shell theory can be given directly in terms of Talmi integrals. We obtain recurrence relations and explicit algebraic expressions for the transformation brackets that will permit their numerical evaluation" :: abstract. 5. MOSHINSKY Borodiansky, Marcos; BARGMANN, V. Group Theory of Harmonic Oscillators. (I). The Collective Modes. From: Nuclear physics 18 (1960) 697-712; North-Holland Publishing Co., Amsterdam. "The present series of papers will deal with the classification of states of N particles moving in a harmonic oscillator common potential. In this paper we will be mainly concerned with the classification scheme that brings out a collective nature of the states. To obtain this collective behaviour, we take advantage of the invariance of the hamiltonian under both ordinary rotations and the unitary group inN dimensions." :: abstract. 6. MOSHINSKY Borodiansky, Marcos; BARGMANN, V. Group Theory of Harmonic Oscillators. (II). The Integrals of Motion for the Quadrupole-Quadrupole Interaction. From: Nuclear Physics 23 (1961) 177-199; North-Holland Publishing Co., Amsterdam. pp. 196-199 separated from staple. [reproduced copy]. 7. MOSHINSKY Borodiansky, Marcos. Wigner Coefficients for the SU3 Group and some Applications. Offprint from: Reviews of Modern Physics, Vol. 34, No. 4, pp. 813-828, October 1962. 8. MOSHINSKY Borodiansky, Marcos. Gelfand States and the Irreducible Representations of the Symmetric Group. Offprint from: Journal of Mathematical Physics, Volume 7, Number 4, pp. 691-698, April 1966. "The set of Gelfand states corresponding to a given partition [h1 . . . hn] form a basis for an irreducible representation of the unitary group Un. The special Gelfand states are defined as those for which [h1 . . . hn] is a partition of n and the weight is restricted to (11 . . . 1). We show that the special Gelfand states constitute basis for the irreducible representations of the symmetric group Sn and use this property to construct explicitly states in configuration and spin-isospin space with definite permutational symmetry." :: abstract. 9. MOSHINSKY Borodiansky, Marcos; Syamala Devi, V. General Approach to Fractional Parentage Coefficients. Offprint from: Journal of Mathematical Physics, Volume 10, Number 3, pp. 455-466, March 1969. Abstract: "The purpose of this paper is to achieve a clearer understanding of the problems involved in the determination of a closed formula for fractional parentage coefficients (fpc). The connection between the fpc and one?block Wigner coefficients of a unitary group of dimension equal to that of the number of states is explicitly derived. Furthermore, these Wigner coefficients are decomposed into ones characterized by a canonical chain of subgroups (for which an explicit formula is given) and transformation brackets from the canonical to the physical chain. It is in the explicit and systematic determination of the states in the latter chain where the main difficulty appears. We fully analyze the case of the p shell to show that a complete nonorthonormal set of states in the physical chain [upsilon] (3)?R(3) can be derived easily using Littlewood's procedure for the reduction of irreducible representations (IR) of SU(3) with respect to the subgroup R(3). This procedure gives a deeper understanding of the free exponent appearing in the polynomials in the creatio.

3 offprints. Original wrappers. From the collection of Abraham Pais. Very good. INVENTORY: 1. RUBINOWICZ, A. Dirac's One-Electron Problem in Momentum Representation. Offprint from: The Physical Review, Vol. 73, No. 11, pp. 1330-1333, June 1, 1948. Signed by Pais. 2. RUBINOWICZ, A. Sommerfeld's Polynomial Method in the Quantum Theory. Offprint from: Indagationes Mathematicae, Vol. XI, Fasc. 2, 1949, & from: Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, Vol. LII, No.4, 1949. Signed by Pais. 3. RUBINOWICZ, Adalbert. Le Rayonnement Multipolaire dans les Spectres Atomiques. From: Le Journal de Physique et le Radium, Serie VIII, Tome X, No. 5, pp. 33-44, Mai 1949. Condition note: brittle paper with considerable chipping. Signed by Pais; inscribed "With best compliments. . ." [not Pais' handwriting]. See: Bibliografie von Adalbert (Wojciech) Rubinowicz (nach âÂÂSelected Papers"), 34a. / Rubinowicz was a Polish theoretical physicist, known for the Maggie-Rubinoqicz representation of Gustav Kirchoff's diffraction formula.

222 x 151 mm. 8vo. Pages (232)-290. [Entire volume: viii, 900 pp.] 5 figs. Quarter cloth, marbled boards, gilt spine; extremities lightly rubbed. Blind stamp of the Carnegie Institution of Washington, Solar Observatory. Fine. This is an important and early paper of Arnold Sommerfeld's. He took his doctoral degree in 1891 with work in methods that were to underlie his most important scientific work in the following decade - the application of the theory of functions of a complex variable to boundary-value problems, especially diffraction phenomena. From 1892 to 1893 he served in the Prussian military, and was Felix Klein's assistant at Gottingen from 1893 to 1896. In 1897 he became professor of mathematics at the Bergakademie in Clausthal. It was here that Sommerfeld applied his extraordinary ingenuity in boundary-value problems to the propagation of electromagnetic waves along wires of finite diameter, obtaining the first rigorous solution, as reported in this paper. Although Sommerfeld never received a Nobel Prize, four of his disciples are Nobel Prize laureates: Peter Debye, Wolfgang Pauli, Linus Pauling, and Werner Heisenberg. The greatest honors Sommerfeld received in his life-time were the chairs of theoretical physics at the University of Vienna (1917) and at the University of Berlin in succession to Max Planck (1927). DSB, XII, pp. 526-527.

Proc. London Math. Soc., 28/599+600+601. - (1897), 8°, pp.395-429, orig. Broschur. First Edition - rare offprint "Extracted from the Proceedings of the London Mathematical Society, Vol.XXVIII., Nos. 599, 600, 601." "In 1896 (Mathematische Theorie der Diffraktion. Math. Ann. 47 (October 1896), 317-374.) Arnold Sommerfeld (1868-1951) obtained an exact closed form solution to the problem of plane wave diffraction by a half plane. He used the method of images on Riemann surfaces corresponding to multivalued solutions of the reduced wave equation, and indicated how this method could be used to obtain exact closed form solution for the problem of diffraction by a wedge. The method of constructing the required many-valued solution of the wave equation was simplified in a subsequent paper, Sommerfeld (1897, Über verzweigte Potentiale in Raum. Proc. Lon. Math. Soc. (1) 28, 395-429.)." A.D. Rawlins, A Green's function for diffraction by a rational wedge. - TR/14/86 October 1986.

Pauli, Wolfgang (1900-1958). On asymptotic series for functions in the theory of diffraction of light. Offprint from Physical Review 54 (1938). 268 x 203 mm. Without wrappers as issued. Creased horizontally, some marginal fraying and chipping, first and last leaves sunned. Good copy. First Edition, Offprint Issue. In 1938 Arnold Sommerfeld, Pauli's former teacher, celebrated his 70th birthday. "For this occasion a special issue of the Annalen der Physik was planned, which, however, was restricted to contributions from 'Aryan' authors. So Pauli and many other of Sommerfeld's pupils living abroad published an issue of the Physical Review; Pauli's contribution was about one of Sommerfeld's favorite subjects in optics" (Enz, No Time to be Brief: A Scientific Biography of Wolfgang Pauli, p. 322). .

Ann. Phys., 3. Folge, 67. - Leipzig, Verlag von Johann Ambrosius Barth, 1899, 8°, pp.233-290, 5 Fig., orig. Broschur. Seltener Separat-Abdruck! Erste Ausgabe dieser wichtigen und frühen Veröffentlichung Sommerfelds. Sie ist die umfangreichste und bedeutendste Arbeit aus seiner Clausthaler Zeit. Das Verhalten der Wellen spielte besonders bei den Experimenten von Hertz eine große Rolle. This is an important and early paper of Arnold Sommerfeld's. He took his doctoral degree in 1891 with work in methods that were to underlie his most important scientific work in the following decade - the application of the theory of functions of a complex variable to boundary-value problems, especially diffraction phenomena. From 1892 to 1893 he served in the Prussian military, and was Felix Klein's assistant at Gottingen from 1893 to 1896. In 1897 he became professor of mathematics at the Bergakademie in Clausthal. It was here that Sommerfeld applied his extraordinary ingenuity in boundary-value problems to the propagation of electromagnetic waves along wires of finite diameter, obtaining the first rigorous solution, as reported in this paper. Although Sommerfeld never received a Nobel Prize, four of his disciples are Nobel Prize laureates: Peter Debye, Wolfgang Pauli, Linus Pauling, and Werner Heisenberg. cf. DSB, XII, pp. 526-527. Arnold Johannes Wilhelm Sommerfeld (1868-1951) war ein deutscher Mathematiker und theoretischer Physiker.

(Leipzig, Ambrosius Barth, 1913). Without wrappers in "Annalen der Physik", Vierte Folge, Bd. 41, No.10. The entire issues offered. Pp. 873-1064 a. 6 plates. Laue's papers: pp. 971-988, pp. 989-1002 a. pp. 1003-1011. With the 5 famous plates in collotype (reproductions of the photographic plates), showing the X-Ray diffraction spectrum of different salt and substances (The "Laue diagram"). These papers represents the first full exposition of Laue's and his co-worker's discovery of the nature of X-Rays. The first two papers were printed the year before in "Münchener Sitzungsberichte", but finds their final form here and with the experimental confirmation by Laue and Tank. He showed that the regular spacing of the atoms in a crystal can serve as a grating of the desired precision, and he measures the wave-lenght of the X-rays.That crystals might be the appropriate grating for the X-rays proved to be well founded when Knipping, Friedrich and Tank found experimental confirmation of the theory."It was in 1895 that Röntgen discovered a new form of radiation, to which, as its nature was so uncertain, he gave the name of the X-ray.It was not until 1912, when von Laue showed it could be diffracted like ordinary light, that it was recognized with certainty as an ether wave of extremely short wave-lenght.Laue used a crystal for his diffraction grating.The X-ray is therefore identical with with light in respect to its nature, but differs greatly in quality: a state of things which is very favourable to an extension of our general knowledge of such radiations."(William Bragg in "The Universe of Light", pp. 228 ff.)."It was the work of Laue and the experiments done by Friedrich and Knipping on his suggestion that cleared up the nature of X rays once and for all and that, moreover, beautifully demonstrated that crystals are composed of atoms arranged in a regular lattice.As in the case of Röntgen's original discovery, the photographs were extremely convincing. Other researchers immediately were attracted by the new field of X-ray spectroscopy and the discoveries by the Braggs and Mosely soon followed."(Siegmund Brandt "The harvest of a Century", Episode 20, p. 80 ff.)."The awarding of the Nobel Prize in physics for 1914 to Laue indicated the significance of the discovery that Albert Einstein called "ONE OF THE MOST BEAUTIFUL IN PHYSICS". Subsequently it was possible to investigate X radiation itself by means of wavelenght determinations as well as to study the structure of the irradiated material. In the truest sense of the word scientists began to cast light on the structure of matter."(DSB VIII, p. 51).PMM: 406 (the first 2 papers in Münchener Sitzungsberichte).The offered issue of "Annalen" contains also an importent paper by P. DEBYE & A. SOMMERFELD: "Theorie des lichtelektrischen Effektes vom Standpunkt des Wirkungsquantums", pp. 873-930.

Math. Ann., 47. - Leipzig, bei G.B. Teubner, gr.- 8°, pp.317-374, 5 Fig., 1 Tafel, orig. Broschur; Eigenhändig "Überreicht v. Verf." und Stempel "Eigenthum des Referenten". Rare Offprint! Arnold Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. The body of Sommerfeld's work is devoted to the systematic development of a method for deriving solutions of the wave equation on Riemann surfaces, a fascinating but perhaps underappreciated topic in mathematical physics. Arnold Johannes Wilhelm Sommerfeld (1868-1951) German mathematician and theoretical physicist, left in 1893 to the University of Göttingen, the centre of mathematical science in Germany at the time. He initially became an assistant at the mineralogical institute there, but his main interests remained mathematics and mathematical physics. In 1894 he became an assistant to the mathematician Felix Klein, who became his scientific role model. He wrote his habilitation thesis Mathematical Theory of Diffraction under him in 1895 and then became a private lecturer in mathematics. He also wrote a book with Klein on the theory of the gyroscope and was commissioned by Klein to write various sections on physics in the Encyclopaedia of Mathematical Sciences. "Seen in the context of previous diffraction analyses, Sommerfeld's 1895 Mathematische Theorie der Diffraction is strikingly original. Starting from Maxwell's electromagnetic field equations, he first formulates a three-dimensional diffraction problem involving a luminous point and an infinitely thin diffracting body. He then extends the domain of the problem from ordinary space to a Riemann double-space. This allows him to write a simple exact solution of the diffraction problem using what is now called the method of images. The method of images requires the function that describes the field due to a luminous point at a general position on the Riemann double-space. For the two-dimensional problems that Sommerfeld considers in detail, the Riemann double-space reduces to a Riemann surface, and thus Sommerfeld must derive the two-dimensional function that describes the wave field due to a luminous point on a Riemann surface. He does this by systematically developing a limit process that relates three-dimensional potential functions and two-dimensional wave functions, and obtains the required wave function on a Riemann surface of n sheets in the form of a complex contour integral and in a series expansion. For the simplest case n = 2, he transforms the complex contour integral into an integral on the real line. He derives numerically useful far-field approximation formulas for this integral, with careful consideration of the approximation error and the spatial regions in which the approximations are valid, and constructs an extraordinary graphical representation. The diffraction solution in the final section is simply an application of the previously derived results. He gives physical interpretations to the various terms of his solution and shows that the formerly distinct entities of incident, reflected, and diffracted light are completely and smoothly unified. With the bravado of youth and genius, he compares his exact solution to the earlier approximate solutions of Poincare and Kirchhoff, and "assigns to each its limited region of validity." "The importance of Sommerfeld's work was quickly recognized. The prominent Gottingen physicist Woldemar Voigt (1850-1919) immediately included a discussion of Sommerfeld's result in the second volume of his .

Debye, Peter J. W. (1884-1966). Zur Theorie der anomalen Dispersion im Gebiete der langwelligen elektrischen Strahlung. Offprint from Verhandlungen der Deutschen Physikalischen Gesellschaft 15 (1913). 777-793pp. 229 x 156 mm. Original printed wrappers, slight wear and toning. Very good to fine. From the library of Walther Gerlach (1889-1979), with his stamp on the front wrapper. First Edition, Offprint Issue. Debye, who trained under Sommerfeld and succeeded Einstein as professor of theoretical physics at the University of Zurich, performed fundamental investigations of the interactions of radiation and matter using x-ray diffraction and other tools, and helped to found modern physical chemistry by developing the fundamental thermodynamics of electrolytic solutions. He received the Nobel Prize for chemistry in 1936 for his contributions to knowledge of molecular structure, and is one of 17 Nobel laureates in chemistry cited by Weber as having performed outstanding work in physics. In chemistry, polarity is a separation of electric charge leading to a molecule having what is known as an electric dipole moment; i.e., a separation of negative and positive charges such that the molecule has negatively and positively charged ends. Debye was the first scientist to study this phenomenon extensively, and his first major scientific contribution was the development of equations relating the electric dipole moment to temperature and the dielectric constant (a dielectric is an insulating material; an insulator's dielectric constant, also known as relative permittivity, measures the ability of that insulator to store electric energy in an electrical field). Prior to Debye's work the dielectric constant of a substance had been written using the Clausius-Mossotti equation, which gave correct values for most substances with small dielectric constants but not for liquids with large dielectric constants. Debye came up with improved equations that "not only represented the behavior of the dielectric constant satisfactorily, but also established the existence of a permanent electric dipole in many molecules and provided a means of determining the moment of the dipole and, from this, the geometry of the molecule. After many years of use in molecular structure investigations, the unit in which the dipole moment was expressed came to be called the 'Debye'" (Dictionary of Scientific Biography). In the present paper, the second of his three important works on this subject, Debye "showed how the orientation of molecular dipoles in a very high frequency alternating field or in a very viscous medium absorbed energy and gave rise to an anomalous dielectric dispersion and dielectric loss" (Dictionary of Scientific Biography). This copy is from the library of Walther Gerlach, co-discoverer of spin quantization in a magnetic field (the "Stern-Gerlach" effect). .

Debye, Peter J. W. (1884-1966) and Arnold Sommerfeld (1868-1951). Theorie des lichtelektrischen Effektes vom Standpunkt des Wirkungsquantums. Offprint from Annalen der Physik, 4th series, 41 (1913). 873-930pp. 222 x 145 mm. Original printed wrappers, a bit chipped, small splits in spine. Very good. From the library of Walther Gerlach (1889-1979), with his characteristic red ink docketing on the front wrapper. First Edition, Offprint Issue. In 1911 Sommerfeld presented his quantum h-hypothesis to explain certain properties of X-radiation, but the hypothesis received criticism at the 1912 Solvay Conference, and Sommerfeld's plan to test the h-hypothesis experimentally was subsequently derailed by von Laue and Knipping's discovery of X-ray diffraction in crystals. "In 1913 Sommerfeld and Debye expanded upon a theory of the photoelectric effect as a last attempt to make the h-hypothesis plausible. They assumed that an atom of metal collects light over a period of time ("accumulation time") until the energy is large enough to emit an electron. Although they were able to derive Einstein's law for the photoelectric effect, the theory amounted to unrealistic conclusions about the accumulation process. Depending on the wavelength of the light with which photoelectrons were emitted, the accumulation time varied widely. X-ray wavelengths amounted to years! Ten years later, when Sommerfeld published the third edition of Atombau und Spektrallinien, he mentioned this absurd result as an example of the futile attempts to marry the quantum theoretical with classical conceptions" (Eckert, Establishing Quantum Physics in Munich: Emergence of Arnold Sommerfeld's Quantum School, pp. 30-31). This copy is from the library of Walther Gerlach, co-discoverer of spin quantization in a magnetic field (the "Stern-Gerlach" effect). .

Nachr. Ges. Wiss. Gött. 1916. - Göttingen 1916, 8°, 11, (1) pp., Rückenbroschur. Rare Offprint! "Göttingen, Phys. Institut, 2. Juni 1916." *) "Sommerfeld, dem ich dieses Resultat mitteilte, schreibt mir in einem Briefe vom 21. Juni, daß er inzwischen auch die geschlossene Formel gefunden habe unter Anwendung der nach Zusatz seiner Arbeit, loc. cit. S.498 abgeänderten Qunantenforderung." Peter Joseph William Debye (1884-1966) Dutch-American physicist and physical chemist, and Nobel laureate in Chemistry. He made outstanding contributions in at least five areas: in the field of quantum physics: Debye theory of the specific heat capacity of matter at low temperatures (see Debye temperature). The Debye theory was one of the first theoretical confirmations of the quantum theory first presented around 10 years earlier. in electrochemistry: (ion activities, Debye radius), in X-ray structure analysis:(Debye-Scherrer method, Debye-Waller factor) in the chemistry of electrolytic solutions:(Debye-Hückel theory) in the microwave spectroscopy of liquids:(Debye function). In his later years as a researcher, he focussed on understanding polymer molecules. In 1936, he was awarded the Nobel Prize in Chemistry 'for his contributions to our knowledge of molecular structures through his research on dipole moments (Debye equation), the diffraction of X-rays and electrons in gases.' He was the originator of the Debye functions named after him, which he used in the Debye theory.

Sommerfeld, Arnold (1868-1951).] Formulierung des Beugungs-Problems. Endlicher Bereich. Carbon typescript with manuscript additions in Sommerfeld's hand. 29ff., numbered 1-27, 27a, 28. 330 x 210 mm. N.p., n.d. (1931). Creased horizontally, some minor marginal fraying and chipping, light soiling. Very good. Carbon typescript of a section of Sommerfeld's "Über die Beugung und Bremsung der Elektronen" (Annalen der Physik 11 [1931]: 257-330), with numerous manuscript equations and other additions in Sommerfeld's hand; the section title can be translated as "Formulation of the diffraction problem: Finite area." Sommerfeld's paper on the diffraction and slowing down of electrons is still cited in current publications on electron microscopy, cosmic ray physics, X-ray tube spectra and related subjects. Sommerfeld, one of the pioneers of atomic and quantum physics, was a brilliant theoretician who introduced the second (azimuthal) quantum number and the fine-structure constant, and pioneered X-ray wave theory. His application of Bohr's revolutionary 1913 theory of the atom to the Zeeman effect and to the fine structure of spectral lines was largely responsible for the rapid and widespread acceptance of Bohr's atomic model. The results of Sommerfeld's investigations of atomic spectra and the Zeeman effect performed during the 1910s and 1920s were accepted almost without change in the post-1925 quantum-mechanical theory of atomic structure. Sommerfeld was equally brilliant as an educator: As the director of the University of Munich's Theoretical Physics Institute, Sommerfeld taught and mentored many of the creators of the new quantum physics, including Nobel Laureates Werner Heisenberg and Wolfgang Pauli. .