Max Born

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Max Born
Max Born.jpg
Max Born (1882–1970)
Born(1882-12-11)11 December 1882
Breslau, German Empire
Died5 January 1970(1970-01-05) (aged 87)
Göttingen, West Germany
ResidenceGöttingen, West Germany
CitizenshipGerman/British
NationalityGerman/British
FieldsPhysics
InstitutionsUniversity of Frankfurt am Main
University of Göttingen
University of Edinburgh
Alma materUniversity of Göttingen
Doctoral advisorCarl Runge
Other academic advisorsWoldemar Voigt
Karl Schwarzschild
Doctoral studentsVictor Frederick Weisskopf
J. Robert Oppenheimer
Lothar Wolfgang Nordheim
Max Delbrück
Walter Elsasser
Friedrich Hund
Pascual Jordan
Maria Goeppert-Mayer
Herbert S. Green
Cheng Kaijia
Siegfried Flügge
Edgar Krahn
Maurice Pryce
Antonio Rodríguez
Bertha Swirles
Paul Weiss
Peng Huanwu[1]
Other notable studentsEmil Wolf
Known forBorn–Haber cycle
Born rigidity
Born coordinates
Born approximation
Born probability
Born–Infeld theory
Born–Oppenheimer approximation
Born's Rule
Born–Landé equation
Born–Huang approximation
Born–von Karman boundary condition
Born equation
Notable awardsNobel Prize in Physics (1954)
Hughes Medal (1950)
Max Planck Medal (1948)
Fellow of the Royal Society (1939)
SpouseHedwig (Hedi) Ehrenberg (m. 1913-1970; his death; 3 children)
Signature
 
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Max Born
Max Born.jpg
Max Born (1882–1970)
Born(1882-12-11)11 December 1882
Breslau, German Empire
Died5 January 1970(1970-01-05) (aged 87)
Göttingen, West Germany
ResidenceGöttingen, West Germany
CitizenshipGerman/British
NationalityGerman/British
FieldsPhysics
InstitutionsUniversity of Frankfurt am Main
University of Göttingen
University of Edinburgh
Alma materUniversity of Göttingen
Doctoral advisorCarl Runge
Other academic advisorsWoldemar Voigt
Karl Schwarzschild
Doctoral studentsVictor Frederick Weisskopf
J. Robert Oppenheimer
Lothar Wolfgang Nordheim
Max Delbrück
Walter Elsasser
Friedrich Hund
Pascual Jordan
Maria Goeppert-Mayer
Herbert S. Green
Cheng Kaijia
Siegfried Flügge
Edgar Krahn
Maurice Pryce
Antonio Rodríguez
Bertha Swirles
Paul Weiss
Peng Huanwu[1]
Other notable studentsEmil Wolf
Known forBorn–Haber cycle
Born rigidity
Born coordinates
Born approximation
Born probability
Born–Infeld theory
Born–Oppenheimer approximation
Born's Rule
Born–Landé equation
Born–Huang approximation
Born–von Karman boundary condition
Born equation
Notable awardsNobel Prize in Physics (1954)
Hughes Medal (1950)
Max Planck Medal (1948)
Fellow of the Royal Society (1939)
SpouseHedwig (Hedi) Ehrenberg (m. 1913-1970; his death; 3 children)
Signature

Max Born (German: [bɔɐ̯n]; 11 December 1882 – 5 January 1970) was a German-born 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 for his "fundamental research in Quantum Mechanics,[2][3] especially in the statistical interpretation of the wave function".[1][4][5][6]. He was the grandfather of actress and singer Olivia Newton John

Born entered the University of Göttingen in 1904, where he found the three renowned mathematicians, Felix Klein, David Hilbert and Hermann Minkowski. He wrote his Ph.D. thesis on the subject of "Stability of Elastica in a Plane and Space", winning the University's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. A chance meeting with Fritz Haber in Berlin in 1918 led to discussion of the manner in which an ionic compound is formed when a metal reacts with a halogen, which is today known as the Born–Haber cycle.

In 1921, Born returned to Göttingen, arranging another chair for his long-time friend and colleague James Franck. Under Born, Göttingen became one of the world's foremost centres for physics. In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. The following year, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation, for which he was awarded the Nobel Prize in 1954. His influence extended far beyond his own research. Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, and Victor Weisskopf all received their Ph.D. degrees under Born at Göttingen, and his assistants included Enrico Fermi, Werner Heisenberg, Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld, Edward Teller, and Eugene Wigner.

In January 1933, the Nazi Party came to power in Germany, and Born, who was Jewish, was suspended. He emigrated to Britain, where he took a job at St John's College, Cambridge, where he wrote a popular science book, The Restless Universe, and Atomic Physics, that soon became a standard text book. In October 1936, he became the Tait Professor of Natural Philosophy at the University of Edinburgh, where, working with German-born assistants E. Walter Kellermann and Klaus Fuchs, he continued his research into physics. Max Born became a naturalised British subject on 31 August 1939, one day before World War II broke out in Europe. He remained at Edinburgh until 1952. He retired to Bad Pyrmont, in West Germany. He died in hospital in Göttingen on 5 January 1970.

Early life[edit]

Max Born was born on 11 December 1882 in Breslau (now Wrocław, Poland), which at the time of Born's birth was part of the Prussian Province of Silesia in the German Empire, to a family of Jewish descent.[7] He was one of two children born to Gustav Born, an anatomist and embryologist, who was a professor of embryology the University of Breslau,[8] and his wife Margarethe (Gretchen) née Kauffmann, from a Silesian family of industrialists. She died when Max was four years old, on 29 August 1886.[9] Max had a sister, Käthe, who was born in 1884, and a half-brother, Wolfgang, from his father's second marriage, to Bertha Lipstein. Wolfgang later became Professor of Art History at the City College of New York.[10]

Initially educated at the König-Wilhelm-Gymnasium in Breslau, Born entered the University of Breslau in 1901. The German university system allowed students to move easily from one university to another, so he spent summer semesters at Heidelberg University in 1902 and the University of Zurich in 1903. Fellow students at Breslau, Otto Toeplitz and Ernst Hellinger, told Born about the University of Göttingen,[11] and Born went there in April 1904. At Göttingen he found three renowned mathematicians: David Hilbert, Felix Klein and Hermann Minkowski. Very soon 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 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 after selecting him to be the first to hold the unpaid, semi-official position of 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.[12][13]

Born's relationship with Klein was more problematic. Born attended a seminar conducted by Klein and professors of applied mathematics, Carl Runge and Ludwig Prandtl, on the subject of elasticity. Although not particularly interested in the subject, Born was obliged to present a paper. Using Hilbert's calculus of variations, he presented one in which, using a curved configuration of a wire with both ends fixed, he demonstrated would be the most stable. Klein was impressed, and invited Born to submit a thesis on the subject of "Stability of Elastica in a Plane and Space" – a subject near and dear to Klein – which Klein had arranged to be the subject for the prestigious annual Philosophy Faculty Prize offered by the University. Entries could also qualify as doctoral dissertations. Born responded by turning down the offer, as applied mathematics was not his preferred area of study. Klein was greatly offended.[14][15]

Klein had the power to make or break academic careers, so Born felt compelled to atone by submitting an entry for the prize. Because Klein refused to supervise him, Born arranged for Carl Runge to be his supervisor. Woldemar Voigt and Karl Schwarzschild became his other examiners. Starting from his paper, Born developed the equations for the stability conditions. As he became more interested in the topic, he had an apparatus constructed that could test his predictions experimentally. In 13 June 1906, the rector announced that Born had won the prize. A month later, he passed his oral examination and was awarded his PhD in mathematics magna cum laude.[16]

On graduation, Born was obliged to perform his military service, which he had deferred while a student. He found himself drafted into the German army, and posted to the 2nd Guards Dragoons "Empress Alexandra of Russia", which was stationed in Berlin. His service was brief, as he was discharged early after an asthma attack in January 1907. He then travelled to England, where he was admitted to Gonville and Caius College, Cambridge, and studied physics for six months at the Cavendish Laboratory under J.J. Thomson, George Searle and Joseph Larmor. After Born returned to Germany, the Army re-inducted him, and he served with the elite 1st (Silesian) Life Cuirassiers "Great Elector" until he was again medically discharged after just six weeks' service. He then returned to Breslau, where he worked under the supervision of Otto Lummer and Ernst Pringsheim, hoping to do his habilitation in physics. A minor accident involving Born's black body experiment, a ruptured cooling water hose, and a flooded laboratory, led to Lummer telling him that he would never become a physicist.[17]

In 1905, Albert Einstein published his paper On the Electrodynamics of Moving Bodies about special relativity. Born was intrigued, and began researching the subject. He was devastated to discover that Minkowski was also researching special relativity along the same lines, but when he wrote to Minkowski about his results, Minkowski asked him to return to Göttingen and do his habilitation there. Born accepted. Toeplitz helped Born brush up on his matrix algebra so he could work with the four-dimensional Minkowski space matrices used in the latter's project to reconcile relativity with electrodynamics. Born and Minkowski got along well, and their work made good progress, but Minkowski died suddenly of appendicitis on 12 January 1909. The mathematics students had Born speak on their behalf at the funeral.[18]

Born attempted to present their results at a meeting of the Göttingen Mathematics Society a few weeks later. He did not get far before he was publicly challenged by Klein and Max Abraham, who rejected relativity, and forced to terminate the lecture. However, Hilbert and Runge were interested in Born's work, and after some discussion with Born they became convinced of the veracity of his results, and persuaded him to give the lecture again. This time he was not interrupted, and Voigt offered to sponsor Born's habilitation thesis.[19] Born subsequently published his talk as an article on "The Theory of Rigid Bodies in the Kinematics of the Relativity Principle" German: Die Theorie des starren Elektrons in der Kinematik des Relativitätsprinzips,[20] which introduced the concept of Born rigidity. On 23 October Born presented his habilitation lecture on the Thomson model of the atom.[21]

Career[edit]

Berlin and Frankfurt[edit]

Born settled in as a young academic at Göttingen as a privatdozent. 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 (another medical student). A frequent visitor to the boarding house was Paul Peter Ewald, a doctoral student of Arnold Sommerfeld on loan to Hilbert at Göttingen as a special assistant for physics. Richard Courant, a mathematician and Privatdozent, called these people the "in group."[22]

In 1912, Born met Hedwig (Hedi) Ehrenberg, the daughter of a University of Leipzig law professor, and a friend of Carl Runge's daughter Iris. She was of Jewish background on her father's side, although he had become a practising Lutheran when he got married, as did Max's sister Käthe. Despite never practising his religion, he refused to convert, and his wedding on 2 August 1913 was a garden ceremony. However, he was baptised as a Lutheran in March 1914 by the same pastor who had performed his wedding ceremony. Born regarded "religious professions and churches as a matter of no importance".[23] His decision to be baptised was made partly in deference to his wife, and partly due to his desire to assimilate into German society.[23] The marriage produced three children: two daughters, Irene, born in 1914, and Margarethe (Gritli), born in 1915, and a son, Gustav, born in 1921. Irene is the mother of British-born Australian singer and actress Olivia Newton-John.[24] Through marriage, Born 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 comedian Ben Elton.[25]

By the end of 1913, Born had published 27 papers, including important work on relativity and the dynamics of crystal lattices,[26] which became a book.[27] In 1914 received a letter from Max Planck explaining that a new professor extraordinarius chair of theoretical physics had been created at the University of Berlin. The chair had been offered to Max von Laue, but he had turned it down. Born accepted.[28] The First World War was now raging. Soon after arriving in Berlin in 1915 he enlisted in an Army signals unit. In October he joined the Artillerie-Prüfungs-Kommission, the Army's Berlin-based artillery research and development organisation, under Rudolf Ladenburg, who had established a special unit dedicated to the new technology of sound ranging. In Berlin, Born formed a lifelong friendship with Einstein, who became a frequent visitor to Born's home.[29] Within days of the armistice in November 1918, Planck had the Army release Born. A chance meeting with Fritz Haber that month led to discussion of the manner in which an ionic compound is formed when a metal reacts with a halogen, which is today known as the Born–Haber cycle.[30]

Even before Born had taken up the chair in Berlin, von Laue had changed his mind, and decided that he wanted it after all.[28] He arranged with Born and the faculties concerned for them to exchange jobs. In April 1919 Born became professor ordinarius and Director of the Institute of Theoretical Physics on the science faculty at the University of Frankfurt am Main.[27] While there, he was approached by the University of Göttingen, which was looking for a replacement for Peter Debye as Director of the Physical Institute.[31] "Theoretical physics," Einstein advised him, "will flourish wherever you happen to be; there is no other Born to be found in Germany today."[32] In negotiating for the position with the education ministry, Born arranged for another chair, of experimental physics, at Göttingen for his long-time friend and colleague James Franck.[31]

Göttingen[edit]

Solvay Conference, 1927. Born is second from the right in the second row, between Louis de Broglie and Niels Bohr.

For the 12 years Born and Franck were at Göttingen from 1921 to 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, but 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, where he completed his habilitation under Born in 1924, and became a privatdozent at Göttingen.[33][34]

In 1925, Born and Heisenberg formulated the matrix mechanics representation of quantum mechanics. On 9 July, Heisenberg gave Born a paper entitled Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen ("Quantum-Theoretical Re-interpretation of Kinematic and Mechanical Relations") to review, and submit for publication. 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.[35][36] When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices,[37] which he had learned from his study under Jakob Rosanes at Breslau University.[38]

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.[39] With the help of his assistant and former student Pascual Jordan, Born began immediately to make a transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper.[40] A follow-on paper was submitted for publication before the end of the year by all three authors.[41] The result was a surprising formulation:

 p q - q p =  { h \over 2 \pi i } I

where p and q were matrices for location and momentum p, and I is the identity matrix. The result arises because matrix multiplication is not commutative.[38] This formulation was entirely attributable to Born, who also established that all the elements not on the diagonal of the matrix were zero. Born considered that his paper with Jordan contained "the most important principles of quantum mechanics including its extension to electrodynamics."[38] The paper put Heisenberg's speculations on a solid mathematical basis. [42]

Even Born was surprised to discover that Paul Dirac had been thinking along the same lines as Heisenberg. Soon Wolfgang Pauli used the matrix method to calculate the energy values of the hydrogen atom, and found that they agreed with the Bohr model. Another important contribution was made by Erwin Schrödinger, who looked at the problem using wave mechanics. This had a great deal of appeal to many at the time, as it offered the possibility of returning to deterministic classical physics. Born would have none of this, as it ran counter to facts determined by experiment.[38] He formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation, which he published in July 1926.[43][42]

In a letter to Born on 4 December 1926, Einstein made his famous remark regarding quantum mechanics:

Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the 'old one'. I, at any rate, am convinced that He is not playing at dice.[44]

This quotation is often paraphrased as 'God does not play dice'.[45]

In 1928, Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics,[46] [47] but Heisenberg alone won the 1932 Prize "for the creation of quantum mechanics, the application of which has led to the discovery of the allotropic forms of hydrogen",[48] while Schrödinger and Dirac shared the 1933 Prize "for the discovery of new productive forms of atomic theory".[48] 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."[49] Heisenberg went on to say that Born and Jordan's contribution to quantum mechanics cannot be changed by "a wrong decision from the outside."[49] In 1954, Heisenberg wrote an article honouring Planck for his insight in 1900, in which he 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."[50]

Those who received their Ph.D. degrees under Born at Göttingen included Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, and Victor Weisskopf.[1][51] 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.[52] Walter Heitler became an assistant to Born in 1928, and completed his habilitation under him in 1929. Born not only recognised talent to work with him, but he "let his superstars stretch past him; to those less gifted, he patiently handed out respectable but doable assignments."[53] Delbrück, and Goeppert-Mayer went on to win Nobel Prizes.[54][55]

Later life[edit]

Born's gravestone in Göttingen is inscribed with the uncertainty principle, which he put on rigid mathematical footing.

In January 1933, the Nazi Party came to power in Germany. In May, Born became one of six Jewish professors at Göttingen who were suspended with pay; Franck had already resigned. In twelve years they had built Göttingen into one of the world's foremost centres for physics.[56] Born began looking for a new job, writing to Maria Göppert-Mayer at Johns Hopkins University and Rudi Ladenburg at Princeton University. Offers soon started to pour in, and he accepted one from St John's College, Cambridge.[57] At Cambridge, he wrote a popular science book, The Restless Universe, and a textbook, Atomic Physics, that soon became a standard text, going through seven editions. His family soon settled into life in England, with his daughters Irene and Gritli becoming engaged to Welshman Brinley (Bryn) Newton-John and Englishman Maurice Price respectively.[58][59]

Born's position at Cambridge was only a temporary one, and his tenure at Göttingen was terminated in May 1935. He therefore accepted an offer from C. V. Raman to come to Bangalore in 1935.[60] Born considered taking a permanent position there, but the Indian Institute of Science did not create an additional chair for him.[61] In November 1935, the Born family had their German citizenship revoked, rendering them stateless. A few weeks later Göttingen cancelled Born's doctorate.[62] Born considered an offer from Pyotr Kapitsa in Moscow, and started taking Russian lessons from Rudolf Peierls's Russian-born wife Genia. But then Charles Galton Darwin asked Born if he would consider becoming his successor as Tait Professor of Natural Philosophy at the University of Edinburgh, an offer that Born promptly accepted,[63] assuming the chair in October 1936.[58]

In Edinburgh, Born promoted the teaching of mathematical physics. He had two German assistants, E. Walter Kellermann and Klaus Fuchs, and together they continued to investigate the mysterious behaviour of electrons.[64] Born became a Fellow of the Royal Society of Edinburgh in 1937, and of the Royal Society of London in March 1939. During 1939, he got as many of his remaining friends and relatives still in Germany as he could out of the country, including his sister Käthe, in-laws Kurt and Marga, and the daughters of his friend Heinrich Rausch von Traubenberg. Hedi ran a Domestic Bureau, placing young Jewish women in jobs. Born received his Certificate of Naturalisation as a British subject on 31 August 1939, one day before the Second World War broke out in Europe.[65]

Born remained at Edinburgh until he reached the retirement age of 70 in 1952. He retired to Bad Pyrmont, in West Germany, in 1954.[66] In October, he received word that he was being awarded the Nobel Prize. His fellow physicists had never stopped nominating him. Franck and Fermi had nominated him in 1947 and 1948 for his work on crystal lattices, and over the years, he had also been nominated for his work on solid state, quantum mechanics and other topics.[67] In 1954, he received the prize for "fundamental research in Quantum Mechanics, especially in the statistical interpretation of the wave function"[5] — something that he had worked on alone.[67] In his Nobel lecture he reflected on the philosophical implications of his work:

I believe that ideas such as absolute certitude, absolute exactness, final truth, etc. are figments of the imagination which should not be admissible in any field of science. On the other hand, any assertion of probability is either right or wrong from the standpoint of the theory on which it is based. This loosening of thinking (Lockerung des Denkens) seems to me to be the greatest blessing which modern science has given to us. For the belief in a single truth and in being the possessor thereof is the root cause of all evil in the world.[68]

In retirement, he continued scientific work, and produced new editions of his books. He died in hospital in Göttingen on 5 January 1970. He was survived by wife Hedi, who died in 1972, and children Irene (mother of the singer Olivia Newton-John), Gritli and Gustav.[66] He is buried in the Stadtfriedhof there, in the same cemetery as Walther Nernst, Wilhelm Weber, Max von Laue, Otto Hahn, Max Planck, and David Hilbert.[69]

Bibliography[edit]

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:

For a full list of his published papers, see HistCite. For his published works, see Published Works – Berlin-Brandenburgische Akademie der Wissenschaften Akademiebibliothek.

Awards and honors[edit]

See also[edit]

Notes[edit]

  1. ^ a b c Max Born at the Mathematics Genealogy Project
  2. ^ Born, M.; Jordan, P. (1925). "Zur Quantenmechanik". Zeitschrift für Physik 34: 858. doi:10.1007/BF01328531.  edit
  3. ^ Born, M. (1926). "Zur Quantenmechanik der Stoßvorgänge". Zeitschrift für Physik 37 (12): 863–867. doi:10.1007/BF01397477.  edit
  4. ^ a b Kemmer, N.; Schlapp, R. (1971). "Max Born 1882-1970". Biographical Memoirs of Fellows of the Royal Society 17: 17. doi:10.1098/rsbm.1971.0002.  edit
  5. ^ a b "The Nobel Prize in Physics 1954". The Official Web Site of the Nobel Prize. Retrieved 10 March 2013. 
  6. ^ O'Connor, John J.; Robertson, Edmund F., "Max Born", MacTutor History of Mathematics archive, University of St Andrews .
  7. ^ Born, G. V. R. (2002). "The wide-ranging family history of Max Born". Notes and Records of the Royal Society 56 (2): 219–262. doi:10.1098/rsnr.2002.0180.  edit
  8. ^ Kemmer & Schlapp 1971, p. 17.
  9. ^ Greenspan 2005, pp. 5–7.
  10. ^ Born 2002, p. 231.
  11. ^ Kemmer & Schlapp 1971, pp. 16–18.
  12. ^ Greenspan 2005, pp. 22–28.
  13. ^ Max Born's Life, Max Born Realschule, retrieved 5 March 2013 
  14. ^ Greenspan 2005, pp. 30–31.
  15. ^ Kemmer & Schlapp 1971, pp. 18–19.
  16. ^ Greenspan 2005, pp. 33–36.
  17. ^ Greenspan 2005, pp. 36–41.
  18. ^ Greenspan 2005, pp. 42–43.
  19. ^ Greenspan 2005, pp. 45-49.
  20. ^ Born, M. (1909). "Die Theorie des starren Elektrons in der Kinematik des Relativitätsprinzips". Annalen der Physik 335 (11): 1–56. doi:10.1002/andp.19093351102.  edit
  21. ^ Greenspan 2005, pp. 45–49.
  22. ^ Greenspan 2005, pp. 49–55.
  23. ^ a b Greenspan 2005, pp. 61–62.
  24. ^ Born 2002, p. 225.
  25. ^ Born 2002, pp. 238–241.
  26. ^ Greenspan 2005, pp. 56–62.
  27. ^ a b Kemmer & Schlapp 1971, p. 20.
  28. ^ a b Greenspan 2005, pp. 63–67.
  29. ^ Greenspan 2005, pp. 70–75.
  30. ^ Greenspan 2005, pp. 83–86.
  31. ^ a b Kemmer & Schlapp 1971, p. 21.
  32. ^ Greenspan 2005, p. 96.
  33. ^ Greenspan 2005, pp. 113, 120, 123.
  34. ^ Jungnickel & McCormmach 1986, pp. 274, 281–285, 350–354.
  35. ^ Heisenberg 1925, pp. 879–893.
  36. ^ Segrè 1980, pp. 153–157.
  37. ^ Pais 1991, pp. 275–279.
  38. ^ a b c d Born, Max (1954). "The Statistical Interpretation of Quantum Mechanics — Nobel Lecture". Official Web Site of the Nobel Prize. Retrieved 9 March 2013. 
  39. ^ Jammer 1966, pp. 206–207.
  40. ^ Born & Jordan 1925, pp. 858–888.
  41. ^ Born, Heisenberg & Jordan 1925, pp. 557–615.
  42. ^ a b Kemmer & Schlapp 1971, p. 35.
  43. ^ Born 1926, pp. 863–867.
  44. ^ Born, Born & Einstein 1971, p. 91.
  45. ^ Born 1969, p. 113.
  46. ^ Bernstein 2005, p. 1004.
  47. ^ Greenspan 2005, p. 190.
  48. ^ a b "Nobel Prize in Physics 1933". Retrieved 9 March 2013. 
  49. ^ a b Greenspan 2005, p. 191.
  50. ^ Greenspan 2005, pp. 285-286.
  51. ^ Greenspan 2005, pp. 142, 262.
  52. ^ Greenspan 2005, pp. 178, 262.
  53. ^ Greenspan 2005, p. 143.
  54. ^ "Max Delbrück – Biography". The Official Web Site of the Nobel Prize. Retrieved 10 March 2013. 
  55. ^ "Maria Goeppert-Mayer – Biography". The Official Web Site of the Nobel Prize. Retrieved 10 March 2013. 
  56. ^ Greenspan 2005, pp. 174–177.
  57. ^ Greenspan 2005, pp. 180-184.
  58. ^ a b Kemmer & Schlapp 1971, p. 22.
  59. ^ Greenspan 2005, pp. 200–201.
  60. ^ Greenspan 2005, p. 199.
  61. ^ Greenspan 2005, pp. 205–208.
  62. ^ Greenspan 2005, p. 224.
  63. ^ Greenspan 2005, pp. 210–211.
  64. ^ Greenspan 2005, pp. 218-220.
  65. ^ Greenspan 2005, pp. 225–226.
  66. ^ a b Kemmer & Schlapp 1971, pp. 23–24.
  67. ^ a b Greenspan 2005, p. 299.
  68. ^ Born 2002, p. 261.
  69. ^ "Stadtfriedhof, Göttingen, Germany". Librairie Immateriel. Retrieved 10 March 2013. 
  70. ^ Greenspan, 2005, pp. 49, 51, and 353.
  71. ^ a b Greenspan, 2005, p. 352.
  72. ^ Greenspan, 2005, pp. 66, 110, and 115.
  73. ^ 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.
  74. ^ Greenspan, 2005, p. 100.
  75. ^ Einstein's Theory of Relativity, Dover Publications, 1962 edition, ISBN 0-486-60769-0.
  76. ^ AIP Niels Bohr Library and AbeBooks: Search on Mechanics of the Atom.
  77. ^ Greenspan, 2005, p. 132.
  78. ^ Problems of Atomic Dynamics is available from MIT Press, ISBN 0-262-52019-2, and Dover Publications, ISBN 0-486-43873-2.
  79. ^ Greenspan, 2005, pp. 159–160.
  80. ^ Jungnickel, Volume 2, 1990, p. 378.
  81. ^ 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.
  82. ^ 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.)
  83. ^ Greenspan, 2005, pp. 174, 292–294.
  84. ^ a b Greenspan, 2005, p. 201.
  85. ^ 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.
  86. ^ The Restless Universe was last published by Dover Publications, 1951, ISBN 0-486-20412-X, but it is no longer in print.
  87. ^ Greenspan, 2005, 245–246
  88. ^ 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.
  89. ^ Physics in My Generation (Springer, 1969), ISBN 0-387-90008-X.
  90. ^ AIP Niels Bohr Library
  91. ^ AIP Niels Bohr Library
  92. ^ The Born–Einstein Letters, Macmillan Publishers, 2004, ISBN 1-4039-4496-2.
  93. ^ 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.
  94. ^ a b c d e f g h Born Biographic Data
  95. ^ 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.
  96. ^ Nobel Biographic Data
  97. ^ "The Born medal and prize". Institute of Physics. Retrieved 30 August 2011. 
  98. ^ "Max-Born-Preis" [Max Born Prize] (in German). German Physical Society. Retrieved 30 August 2011. 
  99. ^ 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.
  100. ^ "Max-Born-Institute for Nonlinear Optics and Short Pulse Spectroskopy - Developement of the MBI". Retrieved 10 March 2009. 

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