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Biographical Memoirs: Volume 64

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Biographical Memoirs: Volume 64 FELIX BLOCH October 23, 1905-September 10, 1983 BY ROBERT HOFSTADTER FELIX BLOCH was a historic figure in the development of physics in the twentieth century. He was one among the great innovators who first showed that quantum mechanics was a valid instrument for understanding many physical phenomena for which there had been no previous explanation. Among many contributions were his pioneering efforts in the quantum theory of metals and solids, which resulted in what are called ''Bloch Waves" or "Bloch States" and, later, "Bloch Walls," which separate magnetic domains in ferromagnetic materials. His name is associated with the famous Bethe-Bloch formula, which describes the stopping of charged particles in matter. The theory of "Spin Waves" was also developed by Bloch. His early work on the magnetic scattering of neutrons led to his famous experiment with Alvarez that determined the magnetic moment of the neutron. In carrying out this resonance experiment, Bloch realized that magnetic moments of nuclei in general could be measured by resonance methods. This idea led to the discovery of nuclear magnetic resonance, which Bloch originally called nuclear induction. For this and the simultaneous and independent work of E. Purcell, Bloch and Purcell shared the Nobel prize in physics in 1952. The aim of the physicist is to carry out and interpret

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Biographical Memoirs: Volume 64 experiments that yield new results. In this sense Bloch reached tremendous heights in both theory and experiment, and it can truly be said that he "made" physics in great leaps and discoveries. In the detailed account of Felix's career which follows, I shall describe these and several other important advances made over the years. But I shall first speak about his background and early life, as he himself described it in a talk he gave at Stanford on January 20, 1970, entitled "How I Became a Physicist." Felix Bloch was born in Zurich on October 23, 1905. This was the same year in which Albert Einstein made three transcendent discoveries in physics. His father was Gustav Bloch, a wholesale grain dealer in Zurich. His mother was Agnes Meyer Bloch, a cousin from Vienna. Gustav came from a large family living in western Bohemia and although he had strong interests in history and languages was unable to attend a university for financial reasons. He moved to Zurich in 1890 to take a position in his uncle's business and became a Swiss citizen. Gustav and Agnes had a daughter in 1902 and, as stated above, Felix was born in 1905. The name "Felix" means "lucky," and it was a propitious way to start out in life with this name. The love of mountains that Felix acquired through vacations in the Alps remained a very deep part of his character all his life. He entered public elementary school when he was six years old. Experiences in school at that tender age were difficult for Felix, who spoke Swiss German with a somewhat different accent than most members of the class. He was also treated rather shabbily by his teacher. This led to a dislike for school, but his sister gave him strong support; when she died at the age of twelve, it was an extremely tragic event for him. Felix led a depressed and isolated life in the years follow-

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Biographical Memoirs: Volume 64 ing the outbreak of World War I. But his feelings changed gradually after moving to a new school where education was governed by the benevolent Pestalozzi method. Arithmetic was a subject that had a special appeal because of its clarity and beauty. He also started music studies and played the piano when he was eight years old. He had a preference for Bach's harmonies. At twelve, Felix finished elementary school and began secondary school. At this time he and his parents made a decision to choose a six-year curriculum that would prepare him for a university. He attended the gymnasium run by the Canton of Zurich, entering in the spring of 1918. This was a very good choice because many of the professors were not only good teachers but were scholars at the same time who had previously earned the title of Ph.D. It was hard work in the gymnasium but his Latin studies were very enjoyable and stimulating. French, English, and Italian were taught, as well as Latin, mathematics, physics, and chemistry. Numbers were especially attractive to Felix and dealing with them instilled a deep respect for quantitative ideas. He applied elementary mathematics, which he had just learned, to astronomy and proved for himself that he could successfully calculate the length of daylight in Zurich at various times of the year. At age fifteen, after three years in gymnasium, Felix started to study physics and continued in gymnasium with languages and mathematics until 1924. He entered the Federal Institute of Technology (ETH) in Zurich in the fall of 1924, having made a choice of engineering as a future profession. This early choice of career is similar to that of Dirac, Wigner, and von Neumann. Following the thorough program of that school, he took calculus and mechanics as well as a course in drafting that he didn't greatly appreciate but was necessary for an engineering degree. During summer vacation he worked in a small iron foundry on the lake of

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Biographical Memoirs: Volume 64 Zurich. This experience provided him with grounds for the decision he needed, and he changed from engineering to physics. His father was rather skeptical of this choice because teaching in high school or working with physics in industry didn't seem to lead to a very promising career. Wishing advice, Felix went to see Professor Hermann Weyl who was the division head for mathematics and physics at the ETH and asked him whether he should study physics. Weyl said ''no," but Bloch did not accept this advice because, as he indicated, he "couldn't help it." In Peter Debye's class in introductory physics Felix found what he desired and felt later that he learned more from that class than from all his other courses together. Coming across Sommerfeld's famous book, Atomic Structure and Spectral Lines, Felix found that he needed to know what was meant by an "electromagnetic field." He did his own reading about that subject and many others in classical physics and made a brief foray into experimental physics that he never completed. On the other hand, he was absorbed by the lectures in the small colloquia held alternately in the departments of the University of Zurich and the ETH. In 1926 an event occurred that had a great influence on his career. He described this in an article for Physics Today in December 1976. He writes: Once at the end of a colloquium I heard Debye saying something like: "Schrödinger, you are not working right now on very important problems anyway. Why don't you tell us some time about that thesis of de Broglie, which seems to have attracted some attention?" So in one of the next colloquia, Schrödinger gave a beautifully clear account of how de Broglie associated a wave with a particle and how he could obtain the quantization rules of Niels Bohr and Sommerfeld by demanding that an integer number of waves should be fitted along a stationary orbit. When he had finished, Debye casually remarked that this way of talking was rather childish. As a student of Sommerfeld he had learned that, to deal properly with waves, one had to have a wave equation. It

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Biographical Memoirs: Volume 64 sounded quite trivial and did not seem to make a great impression, but Schrödinger evidently thought a bit more about the idea afterwards. Just a few weeks later he gave another talk in the colloquium which he started by saying: "My colleague Debye suggested that one should have a wave equation; well I have found one!" And then he told us essentially what he was about to publish under the title "Quantization as Eigenvalue Problem" as the first paper of a series in the Annalen der Physik. I was still too green to really appreciate the significance of this talk, but from the general reaction of the audience I realized that something rather important had happened, and I need not tell you what the name of Schrödinger has meant from then on. Many years later, I reminded Debye of his remark about the wave equation; interestingly enough he claimed that he had forgotten about it and I am not quite sure whether this was not the subconscious suppression of his regret that he had not done it himself. In any event, he turned to me with a broad smile and said: "Well, wasn't I right?" This quotation not only illustrates an important event in Felix's career but demonstrates as well how charmingly he could write and tell stories. A little earlier Felix asked Debye for comments on an idea he had, since it concerned improving an older paper of Debye's on the Compton Effect. Instead Debye suggested that Felix should study Schrödinger's new wave mechanics. Many years later, Felix returned to the Compton Effect and wrote a paper on his original idea, this time using quantum mechanics. Over the next eight years Felix's travels were complex and varied. Aside from short stays he spent extremely productive working periods successively in Leipzig, Zurich, Utrecht, Haarlem, Leipzig again, Copenhagen, Leipzig once more, and Rome before he went to Stanford in 1934. At almost every institution where he stayed, Felix made a major contribution to physics. Some of his achievements over these years are described below. Debye left Zurich in 1927 and became professor at the University of Leipzig in Germany. Once more, taking Debye's

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Biographical Memoirs: Volume 64 advice, Bloch followed him to Leipzig to start graduate work there with Werner Heisenberg, who had just been appointed professor of theoretical physics at the university. Heisenberg was then twenty-six years old and Felix was twenty-two, but Heisenberg was already a famous man. This was a "happy" step, since Heisenberg was one of the discoverers of quantum mechanics, developing his own matrix mechanics approach, and was in a position to apply this new theory to many problems that until then had not been solved. While still in Zurich, Felix had studied Schrödinger's wave theory and learned that the Schrödinger approach and Heisenberg's matrix mechanics were equivalent. Heisenberg had not yet arrived in Leipzig when Felix first went to the University and so he introduced himself to Gregor Wentzel, who was a young professor at that institution. Felix described to Wentzel a calculation he had made on radiation damping of a harmonic oscillator that he thought would moderate the spreading of electron wave packets that followed from the wave theory. When asked for advice, Wentzel suggested that he wasn't an expert and Felix should talk with Heisenberg directly about this calculation. Heisenberg pointed out that the wave would spread in any case, but he encouraged Bloch to complete the calculation for the general case, which he did promptly. This work resulted in Bloch's first paper and, as he later remarked, it was a forerunner of the paper by Weisskopf and Wigner on radiation damping and the natural line widths of spectral lines. Heisenberg took Felix as his first graduate student and suggested that for his thesis Felix should study the conductivity of metals by applying the new quantum mechanical theory. This was a well-known problem in classical theory whose complete solution had baffled such accomplished physicists as Drude, Lorentz, Pauli, and Sommerfeld, even though they had made considerable progress and had ex-

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Biographical Memoirs: Volume 64 plained experimental results concerning the specific heat in metals and the relationship between thermal conductivity and electrical conductivity. This last relationship was known as the Wiedemann-Franz ratio. Classical theory, with some quantum modifications, agreed with experiment, at least approximately, but in these semiclassical treatments, no one understood why the conduction electrons should be treated as an ideal gas of free electrons. By making the assumption of an ideal gas, Pauli had already explained the temperature independence of the paramagnetism of metals by applying Fermi statistics to the conduction electrons. Sommerfeld and Pauli had also produced the results mentioned above for the Wiedemann-Franz ratio as well as for specific heat, but the entire situation about an ideal gas in metals seemed very puzzling. Why the free electron approach worked for metals and why the electrons didn't contribute to the specific heat in solids also needed to be incorporated into any consistent explanation. Felix wrote: When I started to think about it, I felt that the main problem was to explain how the electrons could sneak by all the ions in a metal so as to avoid a mean free path of the order of atomic distances. Such a distance was much too short to explain the observed resistances, which even demanded that the mean free path become longer and longer with decreasing temperature. But Heitler and London had already shown how electrons could jump between two atoms in a molecule to form a covalent bond, and the main difference between a molecule and a crystal was only that there were many more atoms in a periodic arrangement. To make my life easy, I began by considering wave functions in a one-dimensional periodic potential. By straight Fourier analysis I found to my delight that the wave differed from a plane wave of free electron only by a periodic modulation. This was so simple that I didn't think it could be much of a discovery, but when I showed it to Heisenberg he said right away, "That's it." Well, that wasn't quite it yet, and my calculations were only completed in the summer when I wrote my thesis on "The Quantum Mechanics of Electrons in Crystal Lattices."

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Biographical Memoirs: Volume 64 Felix's thesis was published under the title "Uber die Quantenmechanik der Elektronen in Kristallgittern" in the Zeitschrift für Physik (1928). In this work he also calculates the specific heat and electrical resistance of metals. The importance of this paper can hardly be overstated for it provided the basis for the band theory of condensed matter. Out of it followed the formulation by A. H. Wilson of the difference between metals and insulators and the theory of semiconductors. Everyone knows now what this implies for the enormous strides made in our times in radio, television, computers, communications, space exploration, etc., by the replacement of vacuum tubes, with their limited lifetimes, by the long-lived and rugged simplicity of semiconductors. The waves that Felix discovered have been called "Bloch Waves" or "Bloch States," and the concept of these waves turns up everywhere in the theory of condensed matter. Incidentally, the wave solution that Felix discovered was a version of what was known in mathematics as Floquet's Theorem and had been used previously by physicists without realizing its full implications for the quantum mechanics of solids. In 1928, as was customary in those days, Bloch wanted to gain experience in other centers of theoretical physics in Europe, and so he spent the academic year 1928-29 as assistant to Pauli in Zurich. Superconductivity was the main topic that concerned Pauli at the time, and he asked Felix to help in solving that problem which no one had done previously. Pauli was apparently anxious to clean up the subject of superconductivity and even worked on it a bit himself, but Bloch somehow felt that Pauli was not as deeply interested in this as he was in other current problems. Bloch's thesis, in which he introduced waves known by his name, also contains a theory of electrical conductivity in normal metals. One of the results obtained concerned

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Biographical Memoirs: Volume 64 the resistance of metals at low temperature, and it could be observed from this theory that superconductivity could not result from an approach using single electrons. Thus, Bloch could see that one needed something new to explain superconductivity. In the work on superconductivity Bloch contributed an important idea, though he never published it, and we know about it mainly from references by others, such as Bethe, London, Brillouin, and Pauli. Bloch and London pointed out that it was necessary, on thermodynamic grounds, that the superconducting state required a minimum of the energy below the critical temperature but that at temperatures above that point a zero current state is more probable. A theorem, known as Bloch's first theorem on superconductivity, stated that the minimum energy state carried no current, much less a supercurrent. On the other hand, he did realize that the flow of current in the superconducting state involves a correlation between the velocities of the free electrons. But he could make no progress in finding a solution and Bloch's second theorem on superconductivity was humorously stated as, "In the absence of external fields every theory of superconductivity can be disproved." This negative statement, never published by Bloch himself, influenced the work of many others in very constructive ways. Since Bloch never felt he had a successful theory of superconductivity, he did not publish an original article in this field. However, as mentioned above, he had a great influence on the theoretical side of the field through his comments and criticisms of ideas of Bohr, Kronig, Brillouin, and others. Nevertheless, his interest in superconductivity never lagged, and he returned to the subject in the 1960s. His year as Pauli's assistant came to have a lasting influence on his career in physics. Bloch has commented on his early

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Biographical Memoirs: Volume 64 ideas in an article he wrote in 1980 for the Proceedings of the Royal Society of London. He describes his interaction with Pauli and in particular refers to a discussion in which he reminds Pauli that the problem was not as easy as Pauli thought when he gave it to one who had just completed his Ph.D. thesis. Pauli agreed. Felix later remarked that this was an indication that Pauli was "softening up." While serving as Pauli's assistant Bloch also studied the magneto resistance of metals and shortly afterwards attacked the fundamental problems of ferromagnetism. Ferromagnetism had already been treated by Heisenberg, who showed that the basic explanation depended on the exchange interaction of electrons. Heitler and London showed previously that the hydrogen molecule's binding followed from the exchange interaction, and this mechanism offered, at least in principle, a basis for ferromagnetism. Bloch attempted to put Heisenberg's idea into a more rigorous framework. In doing this he showed how it was possible to calculate the exchange energy of a free electron gas and used John Slater's newly invented determinantal formulation of the wave function. His conclusion was that the zero point energy of the electrons figured importantly in determining whether a metal would be ferromagnetic. Slater extended Bloch's calculation at a later time and surmised that the 3d and 4s electrons, rather than the conduction electrons that Bloch studied, could explain ferromagnetism. In the fall of 1929 Bloch went to Utrecht as a Lorentz Foundation fellow, where H. A. Kramers was his host. In November 1929 he published a relatively brief article on the electrical resistivity of metals at low temperature in which he reconsidered a calculation previously made that gave a T3 dependence, where T is the absolute temperature. He included a small term omitted in the first calculation and obtained a T5 law that agreed with experiment.

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Biographical Memoirs: Volume 64 puzzling and hard-to-understand subjects. I think Felix would have been delighted with Walecka's presentation of his original material. I won't discuss his many honors except to say that he was a member of the National Academy of Sciences, the American Academy of Arts and Sciences, the American Philosophical Society, and the extremely prestigious German honor society known as Pour le Mérite. Among the members of this society were Charles Darwin, Carl Friedrich Gauss, Otto Hahn, Werner Heisenberg, Max Planck, Otto Warburg, and Hideki Yukawa, to name just a few illustrious scientists. I would now like to make a few personal remarks. Felix Bloch was a consummate physicist. He had a very deep love of physics, and he was working and thinking about physics up to the last day of his life in 1983. In choosing physics there could hardly have been a better time for him to enter the field, for during the years 1924-27 modern quantum theory emerged in great splendor and he was a witness to it. He rode the crest of the waves of this great new science, contributed to it, and showed how it could be applied to real unsolved problems, such as the conductivity of metals and ferromagnetism. It can truly be said that he was the father of solid-state physics and one of the great physicists of the twentieth century. Felix was many faceted. Besides science he loved music, literature, nature, and particularly mountain climbing and skiing. Once in 1953 he, Leonard Schiff, and I hiked up a mountain in the Mono Recesses of the Sierra to a height of about 13,000 feet. We were all greatly pleased to get to the summit, and this climb remains one of the best memories of my life. A few years ago my wife, Nancy, and I were visiting Lore and Felix in Zurich. On one beautiful day we took a téléférique to the top of a mountain called the Rigi, which

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Biographical Memoirs: Volume 64 could be viewed from their apartment. Families were walking there and brown Swiss cows were grazing, the sounds of their bells floating across the meadows. On the rim of the hill were some young sportsmen preparing hang gliders to take off down the valley. It was the first time any of the four of us had watched this procedure so closely. When they were ready there was a moment's pause. The human glider glanced around, and then took off into space, swooping down over the green valley and soaring in the wind. In the background were the jagged snowy peaks that characterize Switzerland and that Felix loved so much. It was a time to remember—a special time that we all shared. Felix was full of slightly ironic humor. He was a raconteur with many reminiscences of some of the great men of science in our times. His stories transformed those legendary giants of science onto a human scale. Felix admired honesty, intelligence, originality, and kindness. He appreciated eccentricity and was usually tolerant of the idiosyncracies of others. One thing he did not like was an inflated sense of self-importance, and he was not above taking delight in the comeuppance experienced sometimes by those having such a tendency. Although Felix was a convivial man, he sometimes liked solitude. When he was thinking about a difficult problem he would take long walks alone. He and Lore liked coming to our ranch located in a remote area of the Sacramento Valley. Sometimes in the early morning he would be up and out before anyone else, and he could count on not seeing anyone but curious cattle and birds. Later we would all four walk together enjoying the wildflowers and the running creeks in spring or the lush grass of winter. Felix helped in mending fences and bringing in firewood, and his hearty appetite made shared mealtimes a double pleasure. It is very hard right now to think of those times, but

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Biographical Memoirs: Volume 64 we will not forget them. When I came to California in 1949 to do summer work at Berkeley, on the Compton Effect at Ed McMillan's synchrotron, I came to Felix's attention because Leonard Schiff had suggested me as a candidate for a position in the Stanford Physics Department. Felix traveled to the Radiation Laboratory one day to see what I was doing, and there is no doubt that he went there to check on me. I was fascinated to talk with him, and I guess I passed some of his tests, too. As a result I was privileged to know Felix for some thirty-four years. During that time I learned much from him, not only in physics but also about the best things in human companionship. When he worked at his Stanford desk his office door was open 100 percent of the time. I could, and did, see him practically every day and visited with him three or four times a week. I felt I had great rapport with Felix. I don't know if I ever disagreed with him on any matter of consequence, for his thoughts were very lucid and convincing. That is not to say that I was merely absorbing his ideas. Nor does it say that I could keep up with him all the time. But I always did have a fresh way of looking at things after a conversation with him. Felix laid out his thoughts very carefully and would have made a superlative lawyer. When visiting in his office or his home I marveled at how few physics books or journals he had. This illustrates how he worked things out for himself and how his work always had a very personal viewpoint. Felix had extraordinary gifts and he shared them with the world. He had a very honest appreciation of himself and his contributions. He was a man of strong principles and opinions and was direct and outspoken in expressing them. No one had any doubt about where he stood at any time. He had a knack of going to the core of any problem, whether in science, politics, or otherwise. As I have re-

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Biographical Memoirs: Volume 64 marked earlier, he had a superb sense of humor and was often a bit sardonic. He saw through pretension and often enjoyed exposing it. He could see both sides of almost any issue and always tried to see the good side. In 1950 Felix helped me start an electron scattering program at the High Energy Physics Laboratory. I needed the munificent sum of $5,000. Felix arranged a lunch with Ed Ginzton and me during which Felix asked Ed, as director of the laboratory, how big his science budget was for that year. Ed gave him the figure, and Felix remarked with a smile that the support I would need, and for which he asked, wouldn't even be noticed in the total. Ed agreed graciously. During the fifteen years or so I spent on the electron scattering program, I would often come to see Felix after I had worked through the night on a particularly successful run. I would tell him the results. Obviously enjoying what he heard, he would almost always ask a question or make a suggestion that had not occurred to me. This is an example of the exhilarating effect he had on others. Once when Nancy and I visited Felix and Lore in their Zurich apartment, he and I started to talk about Einstein's views on chance, determinism, and quantum mechanics. I ventured the thought that Einstein's view would ultimately prevail. Brusquely he said to me, "Anyone who takes that view doesn't understand quantum mechanics." That sort of bowled me over, but he was right. We continued our discussion, since he never thought I was too dense to recant. I hope this shows how he sometimes expressed his mind. There are some things that I greatly missed in our relationship. For example, I would have liked to have been a musician and to have been able to play music with him. It is a matter of deep regret to me that while he was alive I didn't read his papers with the thoroughness I gave them in preparing this biographical obituary. For I would have

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Biographical Memoirs: Volume 64 told him how much I appreciated and marveled at the depth, elegance, and beauty of his treatments of many fundamental problems in physics. I would have enjoyed listening to how he came upon his ideas and about his conversations with his colleagues on these subjects. I hope he would have enjoyed hearing about how I liked what he did. My last conversation with Felix occurred the day before he and Lore left for Zurich in 1983. I telephoned him at his home from the small conference room in the Stanford Physics Department. There is a smiling picture of him on the wall across the room from the phone. He was looking forward to their trip, and he sounded happy to get my call. That cheery voice together with his smiling face is the way I want to remember Felix Bloch. I miss Felix a great deal. Many of us do. I was among the lucky ones to know him well. He was a friend, ally, mentor, and much more. Felix Bloch died suddenly on September 10, 1983, after suffering a heart attack. He is buried on the side of a mountain that overlooks the city of Zurich. THE AUTHOR WISHES TO express his appreciation to Mrs. Lore Bloch; the Stanford University Archives; and the Niels Bohr Library, Center for History of Physics, at the American Institute of Physics, for access to documentary source material. He wishes also to thank Ms. Lois Nisbet for her help in preparing the manuscript.

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Biographical Memoirs: Volume 64 SELECTED BIBLIOGRAPHY 1928 Zur Strahlungsdampfung in der Quantenmechanik. Phys. Z. 29:58. Uber die Quantenmechanik der Electronen in Kristallgittern. Z. Phys. 52:555. 1929 Bemerkung zur Elektronentheorie des Ferromagnetismus und der electrische Leitfähigkeit. Z. Phys. 57:545. 1930 Zum electrischen Widerstandsgesetz bei Tiefen Temperaturen. Z. Phys. 59:208. Uber die Wechselwirkung der Metallelektronen. In Leipziger Vorträge, ed. P. Debye and S. Hirzel. Zur Theorie des Ferromagnetismus. Z. Phys. 61:206. 1931 With G. Gentile. Zur Anisotropie der Magnetisierung ferromagnetischer Einkristalle. Z. Phys. 70:395. Vorträge und Diskussionen des VII Deutschen Physikertages in Bad Elster. Z. Phys. 32:881. 1932 Zur Theorie der Austausch problems und der Remanenzerscheinung der Feromagnetika. Z. Phys. 74:295. 1933 Zur Bremsung rasch bewegter Teilchen beim Durchgang durch Materie. Ann. Phys. 16:285. Bremsvermögen von Atomen mit mehreren Elektronen. Z. Phys. 81:363. 1934 Contribution to the theory of the Compton Line. Phys. Rev. 46:674. Molekular theorie des Magnetismus Akademische Verlagsgesellschaft M.B.H., Chapter IV, Leipzig.

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Biographical Memoirs: Volume 64 1935 With P. A. Ross. Radiative auger effect. Phys. Rev. 47:884. With C. Møller. Recoil by beta-decay. Nature 136:911. 1936 On the magnetic scattering of neutrons. Phys. Rev. 50:259. On the continuous gamma-radiation accompanying the beta-decay. Phys. Rev. 50:272. 1937 On the magnetic scattering of neutrons II. Phys. Rev. 51:994. With A. Nordsieck. Note on the radiation field of the electron. Phys. Rev. 52:54. 1940 With L. W. Alvarez. A quantitative determination of the neutron moment in absolute nuclear magnetons. Phys. Rev. 57:111. With A. Siegert. Magnetic resonance for nonrotating fields. Phys. Rev. 57:522. 1943 With M. Hamermesh and H. H. Staub. Neutron polarization and ferromagnetic saturation. Phys. Rev. 64:47. 1945 With I. I. Rabi. Atoms in variable magnetic fields. Rev. Mod. Phys. 17:237. 1946 With W. W. Hansen and M. Packard. Nuclear induction. Phys. Rev. 69:127. With W. W. Hansen and M. Packard. Nuclear induction. Phys. Rev. 69:680. With W. W. Hansen and M. Packard. Nuclear induction. Phys. Rev. 70:460. With W. W. Hansen and M. Packard. The nuclear induction experiment. Phys. Rev. 70:474. With R. I. Condit and H. H. Staub. Neutron polarization and ferromagnetic saturation. Phys. Rev. 70:972.

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Biographical Memoirs: Volume 64 1947 With J. H. Van Vleck and M. Hamermesh. Theory of radar reflections from wires or thin metallic strips. J. App. Phys. 18:274. With A. C. Graves, M. Packard, and R. W. Spence. Spin and magnetic moment of tritium. Phys. Rev. 51:373. With A. C. Graves, M. Packard and R. W. Spence. Relative moments of H1 and H3. Phys. Rev. 71:551. With E. C. Levinthal and M. E. Packard. Relative nuclear moments of H1 and H2. Phys. Rev. 72:1125. 1948 With D. Nicodemus and H. H. Staub. A quantitive determination of the magnetic moment of the neutron in units of the proton moment. Phys. Rev. 74:1025. 1950 With C. D. Jeffries. A direct determination of the magnetic moment of the proton in nuclear magnetons. Phys. Rev. 80:305. 1951 Nuclear induction. Physica XVII:272. With L. Brillouin. Electronic theory of the cylindrical magnetron. Advances in Electronics, Vol. III, p. 145. New York: Academic Press. 1953 With R. K. Wangsness. The dynamical theory of nuclear induction. Phys. Rev. 89:728. Experiments on the g-factor of the electron. Physica XIX:821. The principle of nuclear induction. In Les Prix Nobel en 1952. Stockholm: Kungl. Boktryckeriet, P.A. Norstedt och Soner. 1955 Nuclear magnetism. Am. Sci. 41:48. 1956 Dynamical theory of nuclear induction II. Phys. Rev. 102:104. 1957 Generalized theory of relaxation. Phys. Rev. 105:1206.

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Biographical Memoirs: Volume 64 1958 Theory of line narrowing by double-frequency irradiation. Phys. Rev. 111:841. Methods of application of nuclear magnetism. Robert A. Welch Foundation Conferences on Chemical Research, II. Atomic Structure, Chapter V. 1962 With H. E. Rorschach. Energetic stability of persistent currents in a long hollow cylinder. Phys. Rev. 128:1697. 1965 Off-diagonal long range order and persistent currents in a hollow cylinder. Phys. Rev. A 137:787. Some fundamental aspects of NMR. In Nuclear Magnetic Resonance in Chemistry. New York: Academic Press. 1966 Some remarks on the theory of superconductivity. Phys. Today 19(5):27. 1968 Flux quantization and dimensionality. Phys. Rev. 166:415. Simple interpretation of the Josephson effect. Phys. Rev. Lett. 21:1241. 1970 Josephson effect in a superconducting ring. Phys. Rev. B 2:109. 1973 Superfluidity in a ring. Phys. Rev. A 7:2187. 1976 Reminiscences of Heisenberg and the early days of quantum mechanics. Phys. Today 29:23. 1980 Memories of electrons in crystals. Proc. R. Soc. London A 371:24.

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Biographical Memoirs: Volume 64 1982 Dirac equation of the electron in a magnetic field. Phys. Rev. A 25:102. 1987 Past, present and future of nuclear magnetic resonance. In New Directions in Physics. New York: Academic Press. 1989 With J. D. Walecka. Fundamentals of Statistical Mechanics. Stanford, Calif.: Stanford University Press.

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