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BKS theory

From Wikipedia, the free encyclopedia

In the history of quantum mechanics, the Bohr–Kramers–Slater (BKS) theory was perhaps the final attempt at understanding the interaction of matter and electromagnetic radiation on the basis of the so-called old quantum theory, in which quantum phenomena are treated by imposing quantum restrictions on classically describable behaviour.[1][2][3][4] It was advanced in 1924, and sticks to a classical wave description of the electromagnetic field. It was perhaps more a research program than a full physical theory, the ideas that are developed not being worked out in a quantitative way.[5]: 236  The purpose of BKS theory was to disprove Einstein's hypothesis of the light quantum.[6]

One aspect, the idea of modelling atomic behaviour under incident electromagnetic radiation using "virtual oscillators" at the absorption and emission frequencies, rather than the (different) apparent frequencies of the Bohr orbits, significantly led Max Born, Werner Heisenberg and Hendrik Kramers to explore mathematics that strongly inspired the subsequent development of matrix mechanics, the first form of modern quantum mechanics. The provocativeness of the theory also generated great discussion and renewed attention to the difficulties in the foundations of the old quantum theory.[7] However, physically the most provocative element of the theory, that momentum and energy would not necessarily be conserved in each interaction but only overall, statistically, was soon shown to be in conflict with experiment.

Walther Bothe won the Nobel Prize in Physics in 1954 for the Bothe–Geiger coincidence experiment that experimentally disproved BKS theory.[8][9]

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  • Scientist vs. Scientist #4 - Werner Heisenberg and Ernest Rutherford

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Episode number four of scientist versus scientist in this episode we will discuss Werner Heisenberg and Ernest Rutherford first we will discuss Werner Heisenberg Werner Heisenberg was born in Wurzburg Germany on the 5th of December in 1901 his father was Kaspar Earnesta August Heisenberg and his mother was Annie Wecklein both his parents specialized in the study of Greek culture Werner Heisenberg also had an older brother named erwin Heisenberg as a young child eisenberg took a very active interest in playing the piano and by the age of five was able to memorize and play entire songs however his piano lessons were interrupted by his father's Greek philology textbooks which he perused daily his interests slowly turned away from piano and into the sciences Werner and Erwin Heisenberg were raised in a strict but competitive household as their family was in the upper middle class their father did not tolerate laziness and treated both his sons like he treated his students Werner and Erwin Heisenberg constantly competed to outdo each other on assignments particularly math and science assignments given to Erwin in school Werner also competed against himself in sports and would train for hours every week to improve his running his passion for achieving personal goals matured with them into his later life and became a significant part of how he tackled problems in both life and physics in 1910 Eisenberg's family moved to Munich after his father received an appointment to the only professorial chair in Germany for Byzantine philology in Munich Werner attended the mats in millions gymnasium a preparatory school headed by his maternal grandfather and that had been attended by max plank Eisenberg's predecessor in the field of quantum physics the massive millions gymnasium took a more traditional approach to its education and Werner was forced to study more Greek and Latin and less mathematics and physics however when World War one started in nineteen fourteen the school turned its attentions towards a sciences the word took its toll on the Heisenberg family in many ways one way being casper hun Sen Byrd leaving to serve for the Prussian army the Maximilian gymnasium was also forced to make cutbacks on many supplies and one of the school's buildings was turned into barracks for the Bavarian troops urban and Werner Heisenberg were required to labor out in the fields to sustain themselves and their mother despite the efforts of the war Werner Heisenberg completed his education and even went beyond requirements learn calculus at age 16 eisenberg also led a youth group focused on discussing current politics enjoying this separation from the rest of the world in talking about abstract topics the youth group had a significant impact on Heisenberg's intellectual development pushing into question traditional values in to prove things for himself when Werner was 18 he was planning on studying mathematics but decided instead on studying both mathematics in physics after talking to one of the professors at the University of Munich Arnold Summerfield while attending the University of Munich Summerfield became one of his professors alone with Wilhelm wine eisenberg also studied at the University of Gottingen under Matt's born James Frank and David Hilbert while studying at the University he got to meet and work with the world came Polly when Heisenberg come to the University of Munich Summerfield had been working on explaining light emitted by different Adams when given energy Adams would not admit lead have every color on the spectrum but only a select few colors furthermore the late split into groups have lines and then return to the normal spectrum when exposed to a magnetic field this phenomenon was known as the seam in effect after working for a year on the sea minute that eisenberg proposed a new atomic model that effectively explains the minute that however it also contradicted many properties about UMS that both Arnold Summerfield annuals or had proposed earlier and most scientists express just like two words Heisenberg model Werner Heisenberg centrist and physics particularly quantum physics was spurred by his meetings with Neil's bore Arnold Summerfield had known about Heisenberg's interest in Neil's boards lectures and had taken him to abort festival where poor give a series of lectures on quantum physics after the festival boren Heisenberg discussed topics have both science and philosophy and blur became a mentor and close friend to eisenberg in 1923 eisenberg finished his dissertation paper on the topic of hydrodynamics he also took oral exams and both theoretical and experimental physics well his dissertation was not bad the results of his experimental physics is Em's shocked him and as professors eisenberg was ill-prepared for the questions on the exam and could not use a significant number of instruments key to answer any other questions is experimental physics professor was unwilling to give eisenberg his degree but after discussing it with another professor he finally gave Heisenberg a passing grade combined with the stress of examinations eisenberg also had to worry about the political and economical situation in Germany inflation had been taking its toll on German scientists eisenberg included and many were seeking help from america at the time has amber that polished his theory on this the minute that and sent a copy to Neil's bore who invited him to Copenhagen during his time there eisenberg assisted boy with teaching at the University of Copenhagen and worked on his own papers one of the most important %uh pics eisenberg work done well in Copenhagen was his famous uncertainty principle the Heisenberg uncertainty principle states that for a given particle a limited amount of knowledge can be obtained the lotus position and velocity as more knowledge is gained about 10 able less can be known about the other this is attributed to the disturbance when a particle is observed similar to the observer at in the late nineteen twenties and early nineteen thirty's eisenberg worked on atomic structure and properties such as this model the nucleus of an atom in his explanation of ferromagnetism with polly's exclusion principle working with famous physicists such as Albert Einstein neil's blower John Slater and Hunter kramer's he developed the BKS theory on the interaction with matter and electromagnetic waves he also travel to the US China Japan and India to give lectures on quantum physics hun screamer and Heisenberg also collaborated on a paper about disbursement radiation from atoms which are smaller than the wavelength that the radiation as per Heisenberg's reputation have casting a traditional values for new ideas he implemented the virtual oscillator model to calculate spectral frequencies when Heisenberg's friend Max Born read the paper he saw the importance of matrices and highs in birds method this user matrices Burke the use of matrices across many branches of physics particularly atomic physics for his work eisenberg receive the Nobel Prize in Physics in 1932 in 1935 Arnold Summerfield retired from his job his teacher at the University of Munich and nominated December to be his successor however eisenberg was instead put in charge of education for the German nuclear project by the head of the SS although he did not want to work for the SS eisenberg was forced to lecture other workers in the program a nuclear physics and eventually help with that on it bomb himself eisenberg was sent occupied Copenhagen by the nuclear program to collaborate on some the respective nuclear fission though the utilized in the bomb with Neil's bore bore hope to find out as in birds opinion on the project from his visit eisenberg expressed his opinion quite clearly he did no one to help the germans build the atomic bomb him in terms of other scientists have been working on nuclear physics but it was clear that the bomb would not make a great contribution to ending the war in 1945 project also those the American project to investigate whether the Germans had an atomic bomb captured Heisenberg and relocated into facility in France then another in England under Operation epsilon it was transported back to Germany after the war in his last year's eisenberg continued to lecture physics at universities across Europe published papers on topics a physics he had previously done and delve deeper into new topics Werner Heisenberg died on the 1st of February in 1976 at seventy-four years old in Munich for his contributions to science he received the Nobel Prize and the Max Planck battle now let's discuss Ernest Rutherford Ernest Rutherford was born in bright water in New Zealand on the 30th of August in 1871 to James Rutherford and Martha Thompson he had 11 siblings and was the second son James Rutherford was a flat armor and received small paper his job Martha Thompson was a schoolteacher those Rutherford's mother who placed a strong emphasis on education especially the educational earnest in his siblings as a child earnest spent most of his time to me to the phone or doing chores it also spent his free time mostly on the weekends swimming with his brothers he also found creative ways to make money for his family the environment earnest grew up in that that that is later interest in science furnace other ones found earnest outside during a thunderstorm counting seconds to calculate how far away the Lightning was Ernest Rutherford attended the public Fox Hill School at age 10 where he was given his first science textbook rutherford probably attempted to replicate some other experiments done in the book such as constructing miniature Canon heels experimented with the household clock tinkering with disassembling in reconstructing it this teachers at school realized he was fascinated with science and get an extra material on the subject one Rutherford was 11 years old his father moved to overlook to pursue the job a flex million a job that got him more money something the Rutherford family needed as a result James Rutherford those are little to see his children tragedy struck the family after James Rutherford changed jobs feel the children died one from an illness and two from drowning during a fishing trip in 1887 Ernest Rutherford was awarded a scholarship to turn Nelson Collegiate School a private school which overjoyed as mother it tended Nelson collegiate from 1887 to 1889 where it became clear that he had a bright future ahead of him not only was he talkin I love this class is he was an excellent rugby player his success in Nelson collegiate was also spurred on by his principal who gave him books on physics to read in 1890 rutherford received another scholarship this time to Canterbury college in Christchurch similar to Nelson collegiate rutherford excelled at all of his classes at Canterbury and achieved first class honors in math and science he received his Bachelor of Arts and master averse agrees that Canterbury and a Bachelor of Science degree after conducting independent research on electromagnetism that same here he won a third scholarship now for Trinity College in Cambridge England during the first week service did Trinity College rutherford working along with Katie Thompson discovered an easier method of detecting radio waves then Heinrich Hertz his previous method he found that by using magnetizing calls interspersed with Ben's a magnetic iron he could make detecting radio wave simpler in their former commercially viable brother heard in thompson also conducted research on x-rays particularly the effective x-rays on guesses rutherford then studied radioactivity on his own prefer it over the stadium X-rays using uranium and gold oil he's on the 12 radiation compared to treat the gold while another would be absorbed by the name the two types of radiation else for and beta radiation along with naming types of radiation he also created the term half-life after experimenting with the radioactive element the REM in 1900 rutherford left Cambridge to work at McGill University in Canada at McGill he was joined by Frederick Soddy a chemist who was also interested in research in reactivity Saudi in Rutherford worked on identifying the gas that emanated from the radioactive decay ripped aureum they identified it as a new element named Sauron which was later identified as an isotope other another radioactive element redone in 1902 rutherford in saudi published their findings in a paper summing up the work they had done in two years one of the most important topics in the paper discuss the destruction of the items in two different articles which was set to be impossible as Answer considered the indestructible building books the whole matter the paper on atomic disintegration as further heard called it introduce the idea that items could be broken up after the publication of the theory of atomic disintegration rutherford took up work with burt rumble to what on creating a chart for the decay of radioactive elements which they called the decay series the decay series should the decay over radioactive element what it would do came to what radiation a little bit in the half-life of the element rutherford also had to introduce a third candidate K gamma decay that the decay series after moving to Manchester in 1907 rutherford carried out his most famous experiment the gold foil experiment with Hans Geiger in earnest marsdon he fired alpha particles at a piece of gold oil and observed the deflection want some other particles did not make it till his road show that an item did not consist simply have a club electrons but if one center or nucleus with an orbiting clutter the electrons this model that it was the most accurate today and was drawn on by many other scientists to create the current atomic model in his later years rutherford became the first person to trans blue one element into another converting nitrogen into oxygen by bombarding you with alpha particles he also hypothesize the existence of the neutron as a particle to counteract the repulsion between protons in the nucleus which was proven by James Chadwick in 1932 leaving a legacy in the field at nuclear physics Rutherford was the father Atomic Energy and we define the structure the field of physics Ernest Rutherford died on the 19th of October in 1937 at age 66 in Cambridge England for his contributions to science he received the Nobel Prize and the Rumford metal as both the scientists contributed great things to the understanding of physics and left behind a legacy is the a test today the result is a time however you're free to decide on your own opinion thank you for watching this video and as always if you enjoyed leave a lake or a favorite share the video with your friends or you can subscribe for more educational videos check out some of the other videos in the scientists purses sent its series or check at 52 channels peretz for content of

Origins

When Albert Einstein introduced the light quantum (photon) in 1905, there was much resistance from the scientific community. However, when in 1923, the Compton effect showed the results could be explained by assuming the light beam behaves as light-quanta and that energy and momentum are conserved, Niels Bohr was still resistant against quantized light, even repudiating it in his 1922 Nobel Prize lecture. So Bohr found a way of using Einstein's approach without also using the light-quantum hypothesis by reinterpreting the principles of energy and momentum conservation as statistical principles.[10] Thus, it was in 1924 that Bohr, Hendrik Kramers and John C. Slater published a provocative description of the interaction of matter and electromagnetic interaction, historically known as the BKS paper that combined quantum transitions and electromagnetic waves with energy and momentum being conserved only on average.[11][12]

The initial idea of the BKS theory originated with Slater,[13] who proposed to Bohr and Kramers the following elements of a theory of emission and absorption of radiation by atoms, to be developed during his stay in Copenhagen:

  1. Emission and absorption of electromagnetic radiation by matter is realized in agreement with Einstein's photon concept;
  2. A photon emitted by an atom is guided by a classical electromagnetic field (c.f. Louis de Broglie's ideas published September 1923[14]) consisting of spherical waves, thus enabling an explanation of interference;
  3. Even when there are no transitions there exists a classical field to which all atoms contribute; this field contains all frequencies at which an atom can emit or absorb a photon, the probability of such an emission being determined by the amplitude of the corresponding Fourier component of the field; the probabilistic aspect is provisional, to be eliminated when the dynamics of the inside of atoms are better known;
  4. The classical field is not produced by the actual motions of the electrons but by "motions with the frequencies of possible emission and absorption lines" (to be called 'virtual oscillators', creating a field to be referred to as 'virtual' as well).

This fourth point reverts to Max Planck's original view of his quantum introduction in 1900. Planck also did not believe that light was quantized. He believed that a black body had virtual oscillators and that only during interactions between light and the virtual oscillators of the body was the quantum to be considered.[15] Max Planck said in 1911,

Mr. Einstein, it would be necessary to conceive … [of] light waves themselves as atomistically constituted, and hence to give up Maxwell's equations. This seems to me a step which in my opinion is not yet necessary…. I think that first of all one should attempt to transfer the whole problem of the quantum theory to the area of the interaction between matter and radiation.”[16]

Independently, Franz S. Exner had also suggested the statistical validity of energy conservation in the same spirit as the second law of thermodynamics. Erwin Schrödinger, who did his habilitation under the supervision of Exner, was very supportive of the BKS theory. [7] Schrödinger published a paper to provide his own interpretation of the BKS statistical interpretation.[17][7]

Development with Bohr and Kramers

Slater's main intention seems to have been to reconcile the two conflicting models of radiation, viz. the wave and particle models. He may have had good hopes that his idea with respect to oscillators vibrating at the differences of the frequencies of electron rotations (rather than at the rotation frequencies themselves) might be attractive to Bohr because it solved a problem of the latter's atomic model, even though the physical meaning of these oscillators was far from clear. Nevertheless, Bohr and Kramers had two objections to Slater's proposal:

  1. The assumption that photons exist. Even though Einstein's photon hypothesis could explain in a simple way the photoelectric effect, as well as conservation of energy in processes of de-excitation of an atom followed by excitation of a neighboring one, Bohr had always been reluctant to accept the reality of photons, his main argument being the problem of reconciling the existence of photons with the phenomenon of interference;
  2. The impossibility to account for conservation of energy in a process of de-excitation of an atom followed by excitation of a neighboring one. This impossibility followed from Slater's probabilistic assumption, which did not imply any correlation between processes going on in different atoms.

As Max Jammer puts it, this refocussed the theory "to harmonize the physical picture of the continuous electromagnetic field with the physical picture, not as Slater had proposed of light quanta, but of the discontinuous quantum transitions in the atom."[7] Bohr and Kramers hoped to be able to evade the photon hypothesis on the basis of ongoing work by Kramers to describe "dispersion" (in present-day terms inelastic scattering) of light by means of a classical theory of interaction of radiation and matter. But abandoning the concept of the photon, they instead chose to squarely accept the possibility of non-conservation of energy, and momentum.

Experimental counter-evidence

In the BKS paper the Compton effect was discussed as an application of the idea of "statistical conservation of energy and momentum" in a continuous process of scattering of radiation by a sample of free electrons, where "each of the electrons contributes through the emission of coherent secondary wavelets". Although Arthur Compton had already given an attractive account of his experiment on the basis of the photon picture (including conservation of energy and momentum in individual scattering processes), is it stated in the BKS paper that "it seems at the present state of science hardly justifiable to reject a formal interpretation as that under consideration [i.e. the weaker assumption of statistical conservation] as inadequate". This statement may have prompted experimental physicists to improve `the present state of science' by testing the hypothesis of `statistical energy and momentum conservation'. In any case, already after one year the BKS theory was disproved by coincidence methods studying correlations between the directions into which the emitted radiation and the recoil electron are emitted in individual scattering processes. Such experiments were carried independently, with the Bothe–Geiger coincidence experiment performed by Walther Bothe and Hans Geiger,[18][19] as well as the experiment by Compton and Alfred W. Simon.[20][21] They provided experimental evidence pointing in the direction of energy and momentum conservation in individual scattering processes (at least, it was shown that the BKS theory was not able to explain the experimental results). More accurate experiments, performed much later, have also confirmed these results.[22][23]

Commenting on the experiments, Max von Laue considered that “physics was saved from being led astray.”[9]

From the very beginning, Wolfgang Pauli was extremely critical of the BKS theory, referring to it as the Copenhagen putsch (German: Kopenhagener Putsch).[24][9] In a letter to Kramers, Pauli said that Bohr would have abandoned the theory even if no experiment was ever carried out, arguing that it is the notion of motion and forces that needs to be modified, not the conservation of energy.[24] Pauli could not help to mock the theory, proposing to the Institute of Physics in Copenhague to “fly its flag at half mast on the anniversary of the publication of the work of Bohr, Kramers and Slater.”[9]

As suggested by a letter to Max Born,[25] for Einstein, the corroboration of energy and momentum conservation was probably even more important than his photon hypothesis:

Bohr's opinion of radiation interests me very much. But I don't want to let myself be driven to a renunciation of strict causality before there has been a much stronger resistance against it than up to now. I cannot bear the thought that an electron exposed to a ray should by its own free decision choose the moment and the direction in which it wants to jump away. If so, I'd rather be a cobbler or even an employee in a gambling house than a physicist. It is true that my attempts to give the quanta palpable shape have failed again and again, but I'm not going to give up hope for a long time yet.

In light of the experimental results, Bohr informed Charles Galton Darwin that "there is nothing else to do than to give our revolutionary efforts as honourable a funeral as possible".[26]

Bohr's reaction, too, was not primarily related to the photon hypothesis. According to Werner Heisenberg,[27] Bohr remarked:

Even if Einstein sends me a cable that an irrevocable proof of the physical existence of light-quanta has now been found, the message cannot reach me, because it has to be transmitted by electromagnetic waves.

For Bohr the lesson to be learned from the disproof of the BKS theory was not that photons do exist, but rather that the applicability of classical space-time pictures in understanding phenomena within the quantum domain is limited. This theme would become particularly important a few years later in developing the notion of complementarity. According to Heisenberg, Born's statistical interpretation also had its ultimate roots in the BKS theory. Hence, despite its failure the BKS theory still provided an important contribution to the revolutionary transition from classical mechanics to quantum mechanics.

Schrödinger would not abandon the statistical interpretation and would continue to push this theory until the end of his life.[7]

References

  1. ^ Bohr, Niels (1984). The emergence of quantum mechanics (mainly 1924-1926). Niels Bohr Collected Works. Vol. 5. Amsterdam: North-Holland. pp. 3–216. ISBN 978-0-444-86501-4. OCLC 225659653.
  2. ^ J. Mehra and H. Rechenberg, The historical development of quantum theory, Springer-Verlag, New York, etc., 1982, Vol. 1, Part 2, pp. 532-554.
  3. ^ Bohr, N.; Kramers, H.A.; Slater, J.C. (1924). "LXXVI. The quantum theory of radiation". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 47 (281). Informa UK Limited: 785–802. doi:10.1080/14786442408565262. ISSN 1941-5982.
  4. ^ Bohr, N.; Kramers, H. A.; Slater, J. C. (1924). "Über die Quantentheorie der Strahlung". Zeitschrift für Physik (in German). 24 (1). Springer Science and Business Media LLC: 69–87. Bibcode:1924ZPhy...24...69B. doi:10.1007/bf01327235. ISSN 1434-6001. S2CID 120226061.
  5. ^ Pais, Abraham (1991). Niels Bohr's Times: In Physics, Philosophy, and Polity. Oxford University Press. ISBN 0-19-852049-2.
  6. ^ ”How ideas became knowledge: The light-quantum hypothesis 1905–1935” Stephen G. Brush, Historical Studies in the Physical and Biological Sciences, Vol. 37, No. 2 (March 2007), pp. 205-246 (42 pages) Published by: University of California Press, P. 234 “Two physicists who clearly did not accept that claim were Neils Bohr and H. A. Kramers. They were so desperate to rescue the wave theory of light that they were willing to give up the absolute validity of the laws of conservation of energy and momentum in interactions between x-rays and electrons.”
  7. ^ a b c d e Max Jammer, Conceptual Development of Quantum Mechanics, 2e, 1989, p.188
  8. ^ "The Nobel Prize in Physics 1954". NobelPrize.org. Retrieved 2024-02-19.
  9. ^ a b c d Maier, Elke (2011). "Flashback: Particle Billiards, Captured on Film". MaxPlanckResearch. 3: 92–93.
  10. ^ Matrix Theory before Schrodinger: Philosophy, Problems, Consequences, Mara Beller, Isis, Vol. 74, No. 4 (Dec., 1983), pp. 469-491 (23 pages), The University of Chicago Press on behalf of The History of Science Society
  11. ^ Michael Steiner, Ronald Rendell, BKS Showdown over Quanta, The Quantum Measurement Problem (Progress on the Physics of Quantum Measurement) (Volume 1) 1st Edition, chap. 5
  12. ^ Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., chap. 5, 2008.
  13. ^ Letters from J.C. Slater, November, December 1923, reprinted in Ref. 1, pp. 8, 9.
  14. ^ L. de Broglie, Comptes Rendues 177, 507-510 (1923).
  15. ^ Planck to Einstein, 6 July 1907, CPAE, vol. 5, doc. 47, p. 31. “I do not seek the meaning of the quantum of action (light quantum) in the vacuum but at the sites of absorption and emission, and assume that processes in vacuum are described exactly by Maxwell's equations.” This was Max Planck's first known response to Einstein's heuristic theory of light quanta, sent to Einstein in a letter of July 6, 1907.
  16. ^ ”Discussion Following the Lecture: On the Development of Our Views concerning the Nature and Constitution of Radiation,” Physikalische Zeitschrift, vol. 10, pp. 825–826 (1909), presented at the 81st Meeting of the German Scientists and Physicians, September 21, 1909; reprinted in CPAE, vol. 2, doc. 61, pp. 395–398.
  17. ^ Schrödinger, E. (1924-09-01). "Bohrs neue Strahlungshypothese und der Energiesatz". Naturwissenschaften (in German). 12 (36): 720–724. doi:10.1007/BF01504820. ISSN 1432-1904.
  18. ^ Bothe, W.; Geiger, H. (1924). "Ein Weg zur experimentellen Nachprüfung der Theorie von Bohr, Kramers und Slater". Zeitschrift für Physik (in German). 26 (1). Springer Science and Business Media LLC: 44. Bibcode:1924ZPhy...26...44B. doi:10.1007/bf01327309. ISSN 1434-6001. S2CID 121807162.
  19. ^ Bothe, W.; Geiger, H.; Fränz, H.; Kallmann, H.; Warburg, Otto; Toda, Shigeru (1925). "Zuschriften und vorläufige Mitteilungen". Die Naturwissenschaften (in German). 13 (20). Springer Science and Business Media LLC: 440–443. Bibcode:1925NW.....13..440B. doi:10.1007/bf01558823. ISSN 0028-1042. S2CID 23434740.
  20. ^ Compton, A. H. (1 May 1925). "On the Mechanism of X-Ray Scattering". Proceedings of the National Academy of Sciences. 11 (6): 303–306. Bibcode:1925PNAS...11..303C. doi:10.1073/pnas.11.6.303. ISSN 0027-8424. PMC 1085993. PMID 16587006.
  21. ^ Compton, Arthur H.; Simon, Alfred W. (1 August 1925). "Directed Quanta of Scattered X-Rays". Physical Review. 26 (3). American Physical Society (APS): 289–299. Bibcode:1925PhRv...26..289C. doi:10.1103/physrev.26.289. ISSN 0031-899X.
  22. ^ Hofstadter, Robert; Mcintyre, John A. (1 March 1950). "Simultaneity in the Compton Effect". Physical Review. 78 (1). American Physical Society (APS): 24–28. Bibcode:1950PhRv...78...24H. doi:10.1103/physrev.78.24. ISSN 0031-899X.
  23. ^ Cross, William G.; Ramsey, Norman F. (15 December 1950). "The Conservation of Energy and Momentum in Compton Scattering". Physical Review. 80 (6). American Physical Society (APS): 929–936. Bibcode:1950PhRv...80..929C. doi:10.1103/physrev.80.929. ISSN 0031-899X.
  24. ^ a b Enz, Charles P. (1981). "50 years ago Pauli invented the neutrino". Helvetica Physica Acta. 54: 411–418.
  25. ^ Letter of April 29, 1924 in: The Born-Einstein Letters, Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955 with commentaries by Max Born, Walker and Company, New York, 1971.
  26. ^ Pais 1991, p. 238.
  27. ^ Interview with Mehra, quoted in Ref. 2, p. 554
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