F. Bloch

Über die Quantenmechanik der Elektronen in Kristallgittern

ZusammenfassungDie Bewegung eines Elektrons im Gitter wird untersucht, indem wir uns dieses durch ein zunächst streng dreifach periodisches Kraftfeld schematisieren. Unter Hinzunahme der F ermischen Statistik auf die Elektronen gestattet unser Modell Aussagen über den von ihnen herrührenden Anteil der spezifischen Wärme des Kristalls. Ferner wird gezeigt, daß die Berücksichtigung der thermischen Gitterschwingungen Größenordnung und Temperaturabhängigkeit der elektrischen Leitfähigkeit von Metallen in qualitativer Übereinstimmung mit der Erfahrung ergibt.

Zur Theorie des Ferromagnetismus

ZusammenfassungBeim Austauschvorgang der Elektronen im Kristall werden die Eigenfunktionen nullter und Eigenwerte erster Näherung für die Termsysteme hoher Multiplizität bestimmt, wobei die Kopplung zwischen Spin und Bahn vernachlässïgt wird. Sie gestatten, das ferromagnetische Verhalten bei tiefen Temperaturen zu untersuchen und insbesondere die Frage zu beantworten, unter welchen Bedingungen Ferromagnetismus überhaupt möglich ist. Es zeigt, sich, daß dies nur für räumliche Gitter der Fall ist; die Sättigungsmagnetisierung hat dann für tiefe Temperaturen die Form M(T)=M(O) [1 − (T/Θ)3/2].

Bremsvermögen von Atomen mit mehreren Elektronen

ZusammenfassungDas Bremsvermögen komplizierterer Atome wird nach der Methode von Thomas-Fermi berechnet. Es ergibt sich ein einfacher Gang mit der Ordnungszahl, der in gutem Einklang mit der Erfahrung steht.

Zur Anisotropie der Magnetisierung ferromagnetischer Einkristalle

ZusammenfassungDie magnetische Wechselwirkung der Elementarmagnete in ferromagnetischen Einkristallen wird untersucht. Es wird gezeigt, daß für hexagonale Kristalle die magnetische Dipolwechselwirkung der Spins untereinander in erster Näherung und die Wechselwirkung zwischen Spin und Bahn in zweiter Näherung die empirische Abhängigkeit der Energie von der Magnetisierungsrichtung gibt. Bei kubischen Kristallen hingegen wird sie durch die Spinwechselwirkung in erster oder die Spin-Bahn-Wechselwirkung in vierter Näherung gegeben. Eine Abschätzung zeigt, daß dies auch die beobachtete Größenordnung der Effekte richtig wiedergibt.

Heisenberg and the early days of quantum mechanics

It is appropriate in this year, when we celebrate the 50th anniversary of quantum mechanics, and during which we have been saddened by the death of one of its leading founders, Werner Heisenberg, to reminisce about the formative years of the new mechanics. At the time when the foundations of physics were being replaced with totally new concepts I was a student of physics. I sat in the colloquium audience when Peter Debye made the suggestions to Erwin Schrodinger that started him on the study of de Broglie waves and the search for their wave equation. It was from Heisenberg, as his first doctorate student, that I caught the spirit of research, and that I received the encouragement to make my own contributions.

Memories of Electrons in Crystals

As a student in Zurich, it was my good fortune to be present at the colloquium in which Schrödinger told the first time about his wave mechanics. When both he and Debye accepted positions in Germany I decided upon the latter’s advice to continue my studies under Heisenberg in Leipzig, where I arrived in the autumn of 1927. Already in Zurich my interests had turned from experimental to theoretical physics, and particularly towards quantum mechanics, and before coming to Leipzig I had started some calculations on the radiation-damping of wave-packets. As the first thing, Heisenberg encouraged me to complete this work, later published in the Physikalische Zeitschrift, whereupon he considered me ready to start on a topic for my Ph.D. thesis.

Electronic Theory of the Cylindrical Magnetron

Publisher Summary This chapter presents a summary of the theory for cylindrical magnetrons. Solutions of the general equation for “selfconsistent trajectories” in the static case are obtained either by approximations or by numerical integration on the differential analyzer of the Massachusetts Institute of Technology. The magnetron structure is supposed to contain a cylindrical cathode of radius surrounded by a coaxial cylindrical anode of radius with a constant magnetic field in the direction of the axis of symmetry of the structure. The cathode is maintained at potential zero and emits electrons without velocity. In the cylindrical magnetron, only two cases can be realized in a static case: (1) one virtual cathode where all electrons stop and start backwards, and (2) no virtual cathode. The static characteristic of a magnetron is important information to be obtained, since it represents the practical summary needed by the technicians. These characteristics are completely discussed in this chapter and some important results are underlined.

Some remarks on the theory of superconductivity

SUPERCONDUCTIVITY THEORY has been approached in several ways. The most direct but also the most difficult is the attempt to derive all facts from a detailed microscopic theory, and the most significant steps in this direction have been made since 1957 through the theory of John Bardeen, Leon N. Cooper and J. Robert Schreiffer. Another approach, less fundamental but often very instructive, is based on suitably chosen simple models, of which the degenerate ideal Bose gas, suggested by M. R. Schafroth in 1955, has proven to be particularly useful.

Reminiscences of Niels Bohr

This special occasion, I realize, calls for a special selection among the many remarkable instances which the name of Niels Bohr brings back to my mind. It seemed indicated, at first, that I should restrict my account to those reminiscences which bear directly upon specific topics in physics and to omit others of more general human interest. But as I thought more about this talk, I realized that such an omission would present a grossly distorted picture, and that an essential feature of Bohrs character would be lost if one tried to distinguish between the professional and the personal manifestations of his great personality.