Max Born (11 December 1882 – 5 January 1970) was a German-British physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s. Born won the 1954 Nobel Prize in Physics (shared with Walther Bothe).
Max was born on 11 December 1882 in Breslau (now Wrocław, Poland), which at Born's birth was in the Prussian Province of Silesia in the German Empire, to a family of Jewish descent. He was one of two children born to Gustav Born, (b. 22 April 1850, Kempen, d. 6 July 1900, Breslau), an anatomist and embryologist, and Margarethe ('Gretchen') Kauffmann (b. 22 January 1856, Tannhausen, d. 29 August 1886, Breslau), from a Silesian family of industrialists.
Gustav and Gretchen married on 7 May 1881. She died when Max was four years old, on 29 August 1886.
Max had a sister Käthe (b. 5 March 1884), and a half-brother Wolfgang (b. 21 October 1892) from his father's second marriage (m. 13 September 1891) with Bertha Lipstein.
Initially educated at the König-Wilhelm-Gymnasium, Born went on to study at the University of Breslau followed by Heidelberg University and the University of Zurich. During study for his Ph.D.[1] and Habilitation[2] at the University of Göttingen, he came into contact with many prominent scientists and mathematicians including Klein, Hilbert, Minkowski, Runge, Schwarzschild, and Voigt. In 1908-1909 he studied at Gonville and Caius College, Cambridge.
When Born arrived in Göttingen in 1904, Klein, Hilbert, and Minkowski[3] were the high priests of mathematics and were known as the “mandarins.” Very quickly after his arrival, Born formed close ties to the latter two men. From the first class he took with Hilbert, Hilbert identified Born as having exceptional abilities and selected him as the lecture scribe, whose function was to write up the class notes[4] for the students' mathematics reading room at the University of Göttingen. Being class scribe put Born into regular, invaluable contact with Hilbert, during which time Hilbert’s intellectual largesse benefited Born’s fertile mind. Hilbert became Born's mentor and Hilbert eventually selected him to be the first to hold the unpaid, semi-official position of Hilbert’s assistant. Born's introduction to Minkowski came through Born's stepmother, Bertha, as she knew Minkowski from dancing classes in Königsberg. The introduction netted Born invitations to the Minkowski household for Sunday dinners. In addition, while performing his duties as scribe and assistant, Born often saw Minkowski at Hilbert's house. Born’s outstanding work on elasticity – a subject near and dear to Klein – became the core of his magna cum laude Ph.D. thesis, in spite of some of Born’s irrationalities in dealing with Klein.[5]
Born married Hedwig, née Ehrenberg, on 2 August 1913. She was of Jewish descent on her father's side, and was a practicing Lutheran; Born converted from Judaism to the Lutheran faith in 1914. The marriage produced three children, including G. V. R. Born. His daughter Irene was the mother of British-born Australian singer and actress Olivia Newton-John. Via marriage, he is related to jurists Victor Ehrenberg (his father-in-law) and Rudolf von Jhering (his wife's maternal grandfather), as well as Hans Ehrenberg, and is a great uncle of British alternative comedian Ben Elton.
After Max's Habilitation in 1909, he settled in as a young academic at Göttingen as a Privatdozent (Associate Professor).[6] In Göttingen, Born stayed at a boarding house run by Sister Annie at Dahlmannstraße 17, known as El BoKaReBo. The name was derived from the first letters of the last names of its boarders: “El” for Ella Philipson (a medical student), “Bo” for Born and Hans Bolza (a physics student), “Ka” for Theodore von Kármán (a Privatdozent), and “Re” for Albrecht Renner (a medical student). A frequent visitor to the boarding house was Paul Peter Ewald, a doctoral student of Arnold Sommerfeld on loan to David Hilbert at Göttingen as a special assistant for physics.[7] Richard Courant, a mathematician and Privatdozent, called these people the “in group.”[8]
From 1915 to 1919, except for a period in the German army, Born was extraordinarius professor of theoretical physics at the University of Berlin, where he formed a lifelong friendship with Albert Einstein. In 1919, he became ordinarius professor on the science faculty at the University of Frankfurt am Main. While there, the University of Göttingen was looking for a replacement for Peter Debye, and the Philosophy Faculty had Born at the top of their list. In negotiating for the position with the education ministry, Born arranged for another chair at Göttingen and for his long-time friend and colleague James Franck to fill it.[9] In 1921, Born became ordinarius professor of theoretical physics and Director of the new Institute of Theoretical Physics at Göttingen.[10] While there, he formulated[11] the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation of quantum mechanics, published in July 1926[12] and for which he was awarded the Nobel Prize in Physics in 1954, some three decades later.
For the 12 years Born and Franck were at Göttingen (1921–1933), Born had a collaborator with shared views on basic scientific concepts — a distinct advantage for teaching and his research on the developing quantum theory. The approach of close collaboration between theoretical physicists and experimental physicists was also shared by Born at Göttingen and Arnold Sommerfeld at the University of Munich, who was ordinarius professor of theoretical physics and Director of the Institute of Theoretical Physics — also a prime mover in the development of quantum theory. Born and Sommerfeld not only shared their approach in using experimental physics to test and advance their theories, Sommerfeld, in 1922 when he was in the United States lecturing at the University of Wisconsin–Madison, sent his student Werner Heisenberg to be Born’s assistant. Heisenberg again returned to Göttingen in 1923 and completed his Habilitation under Born in 1924 and became a Privatdozent at Göttingen – the year before Heisenberg and Born published their first papers on matrix mechanics.[13][14]
In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. On 9 July, Heisenberg gave Born a paper to review and submit for publication.[15] In the paper, Heisenberg formulated quantum theory avoiding the concrete but unobservable representations of electron orbits by using parameters such as transition probabilities for quantum jumps, which necessitated using two indexes corresponding to the initial and final states.[16] When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices,[17] which he had learned from his study under Jakob Rosanes[18] at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg’s paper.[19] A follow-on paper was submitted for publication before the end of the year by all three authors.[20] (A brief review of Born’s role in the development of the matrix mechanics formulation of quantum mechanics along with a discussion of the key formula involving the non-commutativity of the probability amplitudes can be found in an article by Jeremy Bernstein.[21] A detailed historical and technical account can be found in Mehra and Rechenberg’s book The Historical Development of Quantum Theory. Volume 3. The Formulation of Matrix Mechanics and Its Modifications 1925–1926.[22])
Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics. Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattices theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics.[23]
Born, however, had learned matrix algebra from Rosanes, as already noted, but Born had also learned Hilbert’s theory of integral equations and quadratic forms for an infinite number of variables as was apparent from a citation by Born of Hilbert’s work Grundzüge einer allgemeinen Theorie der Linearen Integralgleichungen published in 1912.[24][25] Jordan, too was well equipped for the task. For a number of years, he had been an assistant to Richard Courant at Göttingen in the preparation of Courant and David Hilbert’s book Methoden der mathematischen Physik I, which was published in 1924.[26] This book, fortuitously, contained a great many of the mathematical tools necessary for the continued development of quantum mechanics. In 1926, John von Neumann became assistant to David Hilbert, and he would coin the term Hilbert space to describe the algebra and analysis which were used in the development of quantum mechanics.[27][28]
In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics,[29] but it was not to be. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933.[30] It was at that time that it was announced Heisenberg had won the Prize for 1932 “for the creation of quantum mechanics, the application of which has led to the discovery of the allotropic forms of hydrogen”[31] and Erwin Schrödinger and Paul Adrien Maurice Dirac shared the 1933 Prize "for the discovery of new productive forms of atomic theory".[31] One can rightly ask why Born was not awarded the Prize in 1932 along with Heisenberg – Bernstein gives some speculations on this matter. One of them is related to Jordan joining the Nazi Party on 1 May 1933 and becoming a Storm Trooper.[32] Hence, Jordan’s Party affiliations and Jordan’s links to Born may have affected Born’s chance at the Prize at that time. Bernstein also notes that when Born won the Prize in 1954, Jordan was still alive, and the Prize was awarded for the statistical interpretation of quantum mechanics, attributable alone to Born.[33]
Heisenberg’s reaction to Born for Heisenberg himself receiving the Prize for 1932 and Born receiving the Prize in 1954 is also instructive in evaluating whether Born should have shared the Prize with Heisenberg. On 25 November 1933 Born received a letter from Heisenberg in which he said he had been delayed in writing due to a “bad conscience” that he alone had received the Prize “for work done in Göttingen in collaboration — you, Jordan and I.” Heisenberg went on to say that Born and Jordan’s contribution to quantum mechanics cannot be changed by “a wrong decision from the outside.”[34] In 1954, Heisenberg wrote an article honoring Max Planck for his insight in 1900. In the article, Heisenberg credited Born and Jordan for the final mathematical formulation of matrix mechanics and Heisenberg went on to stress how great their contributions were to quantum mechanics, which were not “adequately acknowledged in the public eye.”[35]
Those who received their Ph.D. degrees under Born at Göttingen included Max Delbrück, Walter Elsasser, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, J. Robert Oppenheimer, and Victor Weisskopf.[36] Born’s assistants at the University of Göttingen’s Institute for Theoretical Physics included Enrico Fermi, Werner Heisenberg, Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld, Edward Teller, and Eugene Wigner.[36][37][38] Walter Heitler became an assistant to Born in 1928 and under Born completed his Habilitation in 1929.[39] Born not only recognized talent to work with him, but he let his “superstars stretch past him.” [40] His Ph.D. student Delbrück, and six of his assistants (Fermi, Heisenberg, Goeppert-Mayer, Herzberg, Pauli, Wigner) went on to win Nobel Prizes.
In a letter to Born in 1926, Einstein made his famous remark regarding quantum mechanics, often paraphrased as "The Old One does not play dice."[41]
In 1933 Born emigrated from Germany. He had strong and public pacifist opinions; moreover, though Born was a Lutheran, he was classified as a Jew by the Nazi racial laws due to his ancestry, and was thus stripped of his professorship. He took up a position as Stokes Lecturer at the University of Cambridge. From 1936 to 1953 he was Tait Professor of Natural Philosophy at the University of Edinburgh, where he promoted the teaching of mathematical physics. He became a British subject and a Fellow of the Royal Society of London in 1939.[42]
Born had a dislike for nuclear weapons research, but he still acknowledged “it might be the only way out.”[43] Much of the theoretical power behind the development of the first atomic bomb was due to many of those surrounding him at Göttingen and working on atomic physics and quantum mechanics: three of his Ph.D. students (Maria Goeppert-Mayer, Oppenheimer and Weisskopf), three of his assistants (Fermi, Teller, and Wigner), the Director of the Second Institute for Experimental Physics (James Franck), and David Hilbert’s assistant (John von Neumann).[44]
Max and Hedwig Born retired to Bad Pyrmont (10 km south of Hamelin) in West Germany, in 1954.[45]
Born was one of the 11 signatories to the Russell-Einstein Manifesto.
Born died in Göttingen, Germany. He is buried there in the same cemetery as Walther Nernst, Wilhelm Weber, Max von Laue, Max Planck, and David Hilbert.
In memory of his important contributions, the Max Born prize was created by the German Physical Society and the British Institute of Physics. It is awarded annually.
During his life, Born wrote several semi-popular and technical books. His volumes on topics like atomic physics and optics were very well received and are considered classics in their fields which are still in print. The following is a listing of his major works:
- Über das Thomson'sche Atommodell Habilitations-Vortrag (FAM, 1909) - The Habilitation was done at the University of Göttingen, on 23 October 1909.[46]
- Dynamik der Kristallgitter (Teubner, 1915) [47] - After its publication, the physicist Arnold Sommerfeld asked Born to write an article based on it for the 5th volume of the Mathematical Encyclopedia. World War I delayed the start of work on this article, but it was taken up in 1919 and finished in 1922. It was published as a revised edition under the title Atomic Theory of Solid States.[48]
- Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen (Springer, 1920) - Based on Born’s lectures at the University of Frankfurt am Main.[50]
- Available in English under the title Einstein’s Theory of Relativity.[51]
- Vorlesungen über Atommechanik (Springer, 1925) [47]
- Problems of Atomic Dynamics (MIT Press, 1926) – A first account of matrix mechanics being developed in Germany, based on two series of lectures given at MIT, over three months, in late 1925 and early 1926.[53][54]
- Elementare Quantenmechanik (Zweiter Band der Vorlesungen über Atommechanik), with Pascual Jordan. (Springer, 1930) - This was the first volume of what was intended as a two-volume work. This volume was limited to the work Born did with Jordan on matrix mechanics. The second volume was to deal with Erwin Schrödinger’s wave mechanics. However, the second volume was not even started by Born, as he believed his friend and colleague Hermann Weyl had written it before he could do so.[55][56]
- Optik: Ein Lehrbuch der elektromagnetische Lichttheorie (Springer, 1933) - The book was released just as the Borns were emigrating to England.
- Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light,[57] with Emil Wolf. (Pergamon, 1959) - This book is not an English translation of Optik, but rather a substantially new book. Shortly after World War II, a number of scientists suggested that Born update and translate his work into English. Since there had been many advances in optics in the intervening years, updating was warranted. In 1951, Emil Wolf began as Born’s private assistant on the book; it was eventually published in 1959 by Robert Maxwell's Pergamon Press[58] - the delay being due to the lengthy time needed “to resolve all the financial and publishing tricks created by Maxwell.” [59]
- Moderne Physik (1933) -- Based on seven lectures given at the Technischen Hochschule Berlin.[60]
- Atomic Physics (Blackie, London, 1935) - Authorized translation of Moderne Physik by John Dougall, with updates.[61]
- The Restless Universe [62] (Blackie and Son Limited, 1935) - A popularized rendition of the workshop of nature. Born’s nephew, Otto Königsberger, whose successful career as an architect in Berlin was brought to an end when the Nazis took over, was temporarily brought to England to illustrate the book.[60]
- Experiment and Theory in Physics (Cambridge University Press, 1943) – The address given King’s College, Newcastle upon Tyne, at the request of the Durham Philosophical Society and the Pure Science Society. An expanded version of the lecture appeared in a 1956 Dover Publications edition.[63]
- Natural Philosophy of Cause and Chance (Oxford University Press, 1949) – Based on Born’s 1948 Waynflete lectures, given at the College of St. Mary Magdalen, Oxford University. A later edition (Dover, 1964) included two appendices: “Symbol and Reality” and Born’s lecture given at the Nobel laureates 1964 meeting in Landau, Germany.[64]
- A General Kinetic Theory of Liquids with H. S. Green (Cambridge University Press, 1949) -- The six papers in this book were reproduced with permission from the Proceedings of the Royal Society.
- Physics in My Generation: A Selection of Papers (Pergamon, 1956) [65]
- Physik im Wandel meiner Zeit (Vieweg, 1957)
- Physik und Politik (VandenHoeck und Ruprecht, 1960)
- Zur Begründung der Matrizenmechanik, with Werner Heisenberg and Pascual Jordan (Battenberg, 1962) - Published in honor of Max Born’s 80th birthday. This edition reprinted the authors’ articles on matrix mechanics published in Zeitscrift für Physik, Volumes 26 and 33-35, 1924-1926.[66]
- My Life and My Views: A Nobel Prize Winner in Physics Writes Provocatively on a Wide Range of Subjects (Scribner, 1968) - Part II (pp. 63–206) is a translation of Verantwortung des Naturwissenschaftlers.[67]
- Briefwechsel 1916-1955, kommentiert von Max Born with Hedwig Born and Albert Einstein (Nymphenburger, 1969)
- The Born-Einstein Letters: Correspondence between Albert Einstein and Max and Hedwig Born from 1916–1955, with commentaries by Max Born (Macmillan, 1971).[68]
- Mein Leben: Die Erinnerungen des Nobelpreisträgers (Munich: Nymphenburger, 1975). Born's published memoirs.
- My Life: Recollections of a Nobel Laureate (Scribner, 1978).[69] Translation of Mein Leben.
- Born Nobel Prize Speech - 1954
- Born Nobel Prize Lecture - 1954
- Published papers (as listed on the Smithsonian/NASA Astrophysics Data System (ADS))
- Published papers (as listed on HistCite)
- Published Books (based on the Library of Congress citations)
- Published Works - Berlin-Brandenburgische Akademie der Wissenschaften Akademiebibliothek
While links have been provided in this article to journal publications by Born, a few of his papers are worth highlighting here along with citations to translations in English.
Matrix Mechanics A trilogy of papers launched the matrix mechanics formulation of quantum mechanics:
- W. Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen, Zeitschrift für Physik, 33, 879-893, 1925 (received 29 July 1925). [English translation in: B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1 (English title: Quantum-Theoretical Re-interpretation of Kinematic and Mechanical Relations).]
- M. Born and P. Jordan, Zur Quantenmechanik, Zeitschrift für Physik, 34, 858-888, 1925 (received 27 September 1925). [English translation in: B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1 (English title: On Quantum Mechanics).]
- M. Born, W. Heisenberg, and P. Jordan, Zur Quantenmechanik II, Zeitschrift für Physik, 35, 557-615, 1926 (received 16 November 1925). [English translation in: B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1]
Probability Density The now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation of quantum mechanics was published by Born in the first of these two papers, and it is this for which he was awarded the Nobel Prize in Physics in 1954. The second paper is a continuation and extension of the analysis provided in the first paper.
- Jeremy Bernstein Max Born and the Quantum Theory, Am. J. Phys. 73 (11) 999-1008 (2005). Department of Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030. Received 14 April 2005; accepted 29 July 2005.
- Max Born The statistical interpretation of quantum mechanics. Nobel Lecture – 11 December 1954.
- Nancy Thorndike Greenspan, "The End of the Certain World: The Life and Science of Max Born" (Basic Books, 2005) ISBN 0-7382-0693-8. Also published in Germany: Max Born - Baumeister der Quantenwelt. Eine Biographie (Spektrum Akademischer Verlag, 2005), ISBN 3-8274-1640-X.
- Max Jammer The Conceptual Development of Quantum Mechanics (McGraw-Hill, 1966)
- Christa Jungnickel and Russell McCormmach. Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 2: The Now Mighty Theoretical Physics, 1870 to 1925. University of Chicago Press, Paper cover, 1990. ISBN 0-226-41585-6
- Jagdish Mehra and Helmut Rechenberg The Historical Development of Quantum Theory. Volume 3. The Formulation of Matrix Mechanics and Its Modifications 1925–1926. (Springer, 2001) ISBN 0-387-95177-6
- B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1
- Kurt Gottfried, Born to Greatness?, Nature, Vol. 435, 739, 9 June 2005. [1]
- ^ His Ph.D. thesis in mathematics was defended at the University of Göttingen on 13 June 1906: Untersuchungen über die Stabilität der elastischen Linie in Ebene und Raum, unter verschiedenen Grenzbedingungen. It was awarded magna cum laude. See Greenspan, 2005, pp. 35-36 and Max Born’s Life.
- ^ The Habiliation was done at the University of Göttingen, on 23 October 1909: Über das Thomson'sche Atommodell Hablitations-Vortrag (FAM, 1909). See Greenspan, 2005, pp. 49, 51, and 353.
- ^ Hilbert and Minkowski had been colleagues at the University of Königsberg. Klein brought Hilbert to Göttingen. Then, Hilbert brought Minkowski.
- ^ Since the lectures were the creation of the lecturer and not take from a textbook, the scribe performed a very important function.
- ^ Greenspan, 2005, 26-34.
- ^ Greenspan, 2005, pp. 49, 53, and 353.
- ^ It was at the boarding house that Paul Peter Ewald met Ella Philipson, who was to become his wife. They had a daughter, Rose. Hans Bethe, who got his doctorate from Sommerfeld in 1928, met Rose at Duke University in 1937, and they were married in 1938. See Greenspan, 2005, p. 53. Also see Hans Bethe – New York Times.
- ^ Greenspan, 2005, p. 53.
- ^ James Franck took the dual position of ordinarius professor and Director of the Second Institute for Experimental Physics at Göttingen. See Nobel Prize Biography.
- ^ Greenspan, 2005, pp. 96-97.
- ^ Max Born – Nobel Lecture, 11 December 1954: The statistical interpretation of quantum mechanics.
- ^ Max Born (1926). "Zur Quantenmechanik der Stoßvorgänge". Zeitschrift für Physik 37 (12): 863–867. Bibcode 1926ZPhy...37..863B. DOI:10.1007/BF01397477. http://www.springerlink.com/content/h06w8465t710u328/. Retrieved 16 December 2008.
- ^ Greenspan, 2005, pp. 113, 120, and 123.
- ^ Jungnickel, Christa and Russell McCormmach. Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 2: The Now Mighty Theoretical Physics, 1870 to 1925. University of Chicago Press, Paper cover, 1990. ISBN 0-226-41585-6. pp. 274, and 281-285 and 350-354.
- ^ W. Heisenberg, Über quantentheoretishe Umdeutung kinematisher und mechanischer Beziehungen, Zeitschrift für Physik, 33, 879-893, 1925 (received 29 July 1925). [English translation in: B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1 (English title: “Quantum-Theoretical Re-interpretation of Kinematic and Mechanical Relations”).]
- ^ Emilio Segrè, From X-Rays to Quarks: Modern Physicists and their Discoveries (W. H. Freeman and Company, 1980) ISBN 0-7167-1147-8, pp. 153–157.
- ^ Abraham Pais, Niels Bohr’s Times in Physics, Philosophy, and Polity (Clarendon Press, 1991) ISBN 0-19-852049-2, pp. 275–279.
- ^ Max Born — Nobel Lecture (1954)
- ^ M. Born and P. Jordan, Zur Quantenmechanik, Zeitschrift für Physik, 34, 858–888, 1925 (received 27 September 1925). [English translation in: B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1]
- ^ M. Born, W. Heisenberg, and P. Jordan, Zur Quantenmechanik II, Zeitschrift für Physik, 35, 557-615, 1925 (received 16 November 1925). [English translation in: B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1]
- ^ Jeremy Bernstein Max Born and the Quantum Theory, Am. J. Phys. 73 (11) 999–1008 (2005)
- ^ Mehra, Volume 3 (Springer, 2001)
- ^ Jammer, 1966, pp. 206-207.
- ^ van der Waerden, 1968, p. 51.
- ^ The citation by Born was in Born and Jordan's paper, the second paper in the trilogy which launched the matrix mechanics formulation. See van der Waerden, 1968, p. 351.
- ^ Constance Ried Courant (Springer, 1996) p. 93.
- ^ John von Neumann Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren, Mathematische Annalen 102 49–131 (1929)
- ^ When von Neumann left Göttingen in 1932, his book on the mathematical foundations of quantum mechanics, based on Hilbert’s mathematics, was published under the title Mathematische Grundlagen der Quantenmechanik. See: Norman Macrae, John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More (Reprinted by the American Mathematical Society, 1999) and Constance Reid, Hilbert (Springer-Verlag, 1996) ISBN 0-387-94674-8.
- ^ Bernstein, 2004, p. 1004.
- ^ Greenspan, 2005, p. 190.
- ^ a b Nobel Prize in Physics and 1933 – Nobel Prize Presentation Speech.
- ^ Bernstein, 2005, p. 1004.
- ^ Bernstein, 2005, p. 1006.
- ^ Greenspan, 2005, p. 191.
- ^ Greenspan, 2005, pp. 285-286.
- ^ a b Sources for History of Quantum Physics
- ^ Greenspan, 2005, pp. 178 and 262.
- ^ Biography on Gerhard Herzberg - National Sciences and Engineering Research Council of Canada
- ^ Author Catalog: Heitler – American Philosophical Society
- ^ Greenspan, 2005, p. 143.
- ^ Letter from A. Einstein to M. Born dated 12 December 1926 [Max Born, Physics in my generation, Springer-Verlag, New York (1969), p. 113]. Also: "…Even the great initial success of the quantum theory does not make me believe in the fundamental dice-game…" — Albert Einstein, 7 September 1944 (p. 149). The Correspondence between Albert Einstein and Max and Hedwig Born 1916-1955 with commentaries by Max Born, ISBN 0-8027-0326-7
- ^ Born was elected to the Royal Society in March and received his Certificate of Naturalization on 31 August 1939, one day before World War II broke out in Europe. See Greenspan, 2005, p. 226.
- ^ Greenspan, 2005, p. 239.
- ^ Students, assistants, and colleagues of Born at Göttingen who worked on the Manhattan Project:
- Maria Goeppert-Mayer – Worked on the Manhattan Project with Harold Urey at Columbia University on isotope separation.
- Robert Oppenheimer – Director of Los Alamos Scientific Laboratory (LASL) - One of the four major sites of the Manhattan Engineering District.
- Victor Weisskopf – Head of T-3 Group, Experiments, Efficiency Calculations, and Radiation Hydrodynamics, LASL
- Enrico Fermi – Director of Research, Met Lab of the University of Chicago - One of the four major sites of the Manhattan Engineering District.
- Edward Teller – Head of T-1 Group, Hydrodynamics of Implosion and Super, LASL
- Eugene Wigner – Director of Theoretical Studies, Met Lab
- James Franck – Director of the Chemistry Division, Met Lab, and Chairman of the Committee on Political and Social Problems
- John von Neumann – LASL consultant on implosion mechanism for the plutonium bomb. (Neumann was assistant to David Hilbert at Göttingen and was greatly influenced by both David Hilbert’s and Max Born’s work. Neumann applied the mathematics of Hilbert space to Born’s quantum mechanics, and, in 1932, his foundational book on the mathematical underpinnings of quantum mechanics, Mathematische Grundlagen der Quantenmechanik, was published.)
- ^ Biographical Sketch from the German Historical Museum
- ^ Greenspan, 2005, pp. 49, 51, and 353.
- ^ a b Greenspan, 2005, p. 352.
- ^ Greenspan, 2005, pp. 66, 110, and 115.
- ^ A new edition of Dynamical Theory of Crystal Lattices is available from Oxford University Press in hard cover ISBN 978-0-19-850369-9 and in soft cover ISBN 0-19-850369-5.
- ^ Greenspan, 2005, p. 100.
- ^ Einstein’s Theory of Relativity, Dover Publications, 1962 edition, ISBN 0-486-60769-0.
- ^ AIP Niels Bohr Library and AbeBooks: Search on Mechanics of the Atom.
- ^ Greenspan, 2005, p. 132.
- ^ Problems of Atomic Dynamics is available from MIT Press, ISBN 0-262-52019-2, and Dover Publications, ISBN 0-486-43873-2.
- ^ Greenspan, 2005, pp. 159-160.
- ^ Jungnickel, Volume 2, 1990, p. 378.
- ^ Principles of Optics is now in its 7th revised printing, ISBN 0-521-64222-1. The first 5 revised editions were done by Pergamon Press (1959 - 1975). The last 2 were done by Cambridge University Press in 1980 and 1999.
- ^ Paul Rosbaud, a former editor at Springer who remained in Germany during World War II and spied for the allies, was initially involved with Born and the endeavor to publish Optik in English, as Rosbaud was organizing a publishing company in England after the war. The publishing company did not materialize, and Rosbaud eventually joined Pergamon Press. (Greenspan, 2005, pp. 292-294.)
- ^ Greenspan, 2005, pp. 174, 292-294.
- ^ a b Greenspan, 2005, p. 201.
- ^ The eighth edition was published in 1969, including revisions by R. J. Blin-Stoyle & J. M. Radcliffe. The 8th edition of Atomic Physics is available from Dover Publications in paper cover, ISBN 0-486-65984-4.
- ^ The Restless Universe was last published by Dover Publications, 1951, ISBN 0-486-20412-X, but it is no longer in print.
- ^ Greenspan, 2005, 245-246 and AbeBooks
- ^ Citations for Max Born Based on the Library of Congress - See the entry for Natural Philosophy of Cause and Chance. Also see Greenspan, 2005, p. 352.
- ^ Physics in My Generation (Springer, 1969), ISBN 0-387-90008-X.
- ^ AIP Niels Bohr Library
- ^ AIP Niels Bohr Library
- ^ The Born-Einstein Letters, Macmillan Publishers, 2004, ISBN 1-4039-4496-2.
- ^ My Life: Recollections of a Nobel Laureate was also published by Taylor and Francis/Charles Scribner's Sons, ISBN 0-85066-174-9. No longer in print.
- ^ a b c d e f g h Born Biographic Data
- ^ The award was presented for research on quantum mechanics of fields and shared with Born's collaborator H. W. Peng. See Greenspan, 2005, p. 257 and Born Biographic Data.
- ^ Nobel Biographic Data
- ^ James Franck und Max Born in Göttingen: Reden zur akademischen Feier aus Anlass der 100. Wiederkehr ihres Geburtsjahres. (Vandenhoeck & Ruprecht, 1983). Speeches by Norbert Kamp, Peter Haasen, Gerhart W. Rathenau, and Friedrich Hund. Franck was Director of the Second Institute for Experimental Physics at Göttingen, while Born was Director of the Institute of Theoretical Physics.
- American Institute of Physics History Search: Max Born
- Encyclopaedia Britannica, Max Born - full article
- Annotated bibliography for Max Born from the Alsos Digital Library for Nuclear Issues
- Freeview video of Gustav Born (son of Max) with conversation and film on Gustav's memories of his father by the Vega Science Trust
- O'Connor, John J.; Robertson, Edmund F., "Max Born", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Born.html .
- Max Born’s Life
- Max Born at the Mathematics Genealogy Project
- Max Born information from Nobel Winners site
- Nobel Laureate biography
- Papers of Professor Max Born (1882-1970) Held at the Edinburgh University Library, Special Collections Division
- Recollections of Max Born, by Emil Wolf, in Astrophysics and Space Science, Volume 227, Numbers 1-2. (Biographical tribute)
- Kuhn, Thomas S., John L. Heilbron, Paul Forman, and Lini Allen Sources for History of Quantum Physics (American Philosophical Society, 1967)
- Oral History interview transcript with Max Born June 1960, 17 & 18 October 1962, American Institute of Physics, Niels Bohr Library and Archives
