Arnold Johannes Wilhelm Sommerfeld (sinh ngay 5 thang 12 nam 1868 – mat ngay 26 thang 4 nam 1951) la nha vat ly ly thuyet nguoi Đuc co đong gop tien phong trong nganh vat ly nguyen tu va vat ly luong tu, la nguoi đa đao tao rat nhieu nha khoa hoc cho thoi đai moi cua nganh vat ly ly thuyet. Ong la nguoi đua ra hang so α (hang so cau truc tinh te) cho vat ly luong tu.


Viec hoc Sommerfeld hoc toan va vat ly tai đai hoc Konigsberg (đai hoc Albertina) o que nha la thanh pho Konigsberg thuoc Đong Pho. Thay huong dan luan van cho ong la nha toan hoc Ferdinand von Lindemann. Ong cung huong loi do đuoc hoc voi cac nha toan hoc Adolph Hurwitz, David Hilbert, va nha vat ly Emil Wiechert. Ong tham gia hoi sinh vien Burschenschaft Đuc, ve sau đa lam mat ong co mot vet seo do đau kiem. Ong nhan hoc vi tien si khoa hoc nam 1891.
Sau khi nhan bang tien si Sommerfeld o lai Konigsberg day lop diploma. Nam 1892 ong vuot qua ki thi toan quoc đe phuc vu mot nam trong quan đoi tai trung đoan du bi đong ngay Konigsberg. Ong hoan thanh nghia vu quan su thang 9 nam 1893 nhung van tinh nguyen tham gia quan ngu tam tuan trong suot tam nam ke tiep. Do the hinh khoe manh, co seo tren mat va lai đe ria kem rau kieu Pho nen trong ong an tuong nhu the la mot đai ta bo binh.


Su nghiep = O đai hoc Gottingen =
Thang 10 nam 1893 ong đen lam viec tai đai hoc Gottingen bay gio la trung tam cua nen toan hoc Đuc, tro thanh phu ta cho giao su Theodor Liebisch nguoi tung day tai đai hoc Konigsberg va la than huu cua gia đinh Sommerfeld.
Thang 9 nam 1894 ong bat đau lam phu ta cho nha toan hoc Felix Klein, chuyen viet nhung ghi chu bao quat trong bai giang cua Klein roi trinh bay lai cho "Phong đoc toan hoc" đong thoi đieu hanh phong đoc nay. Luan van hau tien si cua ong do Klein huong dan hoan tat nam 1895 đa giup ong tro thanh giao su đai hoc Gottingen. Ong giang day rat nhieu chu đe toan hoc va vat ly toan, trong đo bai giang ve phuong trinh đao ham rieng cua ong la đau tien ve chu đe nay đuoc giang tai Gottingen  ma sau nay đuoc phat trien thanh tap 6 tua "Phuong trinh đao ham rieng trong vat ly" thuoc bo giao trinh "Bai giang vat ly ly thuyet".
Bai giang cua Klein ve vat the xoay nam 1895 va 1896 dan đen cong trinh bon tap tua Die Theorie des Kreisels do Klein va Sommerfeld cung viet chung trong 13 nam tu nam 1897 đen 1910. Hai tap đau co noi dung ly thuyet, con hai tap sau viet ve ung dung cho nganh đia vat ly, thien van va cong nghe. Nhung nam cong tac cung Klein đa anh huong len ong khien ong bat đau quan tam nhieu hon đen toan hoc ung dung va nghe thuat giang day.
Thoi gian nay ong quen ba Johanna Hopfner la con gai cua mot uy vien ban quan tri đai hoc Gottingen ten Ernst Hopfner. Thang 10 nam 1897 ong đuoc bo nhiem lam truong bo mon toan tai Bergakademie, Clausthal-Zellerfeld ke nhiem Wilhelm Wien. Vi tri nay giup ong đam bao thu nhap đe co the ket hon ba Johanna.
Do đe nghi cua Klein, ong lam bien tap cho quyen thu nam trong bo Encyklopadie der mathematischen Wissenschaften cung la mot viec chinh ong đa lam tu nam 1898 đen 1926.


= O đai hoc Aachen =
Tu nam 1900 nho su no luc cua giao su Felix Klein, ong đuoc bo nhiem chuc giao su truong khoa toan ung dung tai đai hoc RWTH Aachen.Tai đay ong theo đuoi va phat trien ly thuyet ve thuy đong luc hoc trong mot thoi gian dai, roi sau nay cac hoc tro cua ong nhu Ludwig Hopf va Werner Heisenberg tai đai hoc Munich cung viet luan van tien si trong linh vuc đo.


= O đai hoc Munich =

Tu nam 1906, ong la giao su vat ly kiem giam đoc Vien vat ly ly thuyet moi thanh lap o đai hoc Munich do ong Wilhelm Rontgen truong khoa vat ly cua truong bo nhiem.
Đen cuoi the ki 19 đau the ki 20, nganh vat ly thuc nghiem đa đuoc đanh gia cao nhieu hon truoc trong cong đong khoa hoc Đuc. Tuy nhien nhung nha ly thuyet nhu Sommerfeld hay Max Born tai đai hoc Gottingen do co nen tang tu toan hoc nen muon đua vat ly toan thanh mui phat trien uu tien, con vat ly thuc nghiem la đe kiem nghiem va phat trien ly thuyet. Sau khi hoan tat bang tien si voi Sommerfeld, Wolfgang Pauli, Werner Heisenberg, va Walter Heitler tro thanh phu ta cua Born roi ho gop phan quan trong vao su phat trien vu bao cua nganh co hoc luong tu.
Trong 32 nam o đai hoc Munich, ong giang day nhieu khoa hoc co ban cung nhu chuyen sau, to chuc seminar. Cac khoa co ban gom co hoc, co hoc ve vat the bien dang, đien đong luc hoc, quang hoc, nhiet đong luc hoc, co hoc thong ke, phuong trinh đao ham rieng trong vat ly, đuoc mo mot tuan bon gio trong 13 tuan mua đong va 11 tuan mua xuan cho sinh vien đa hoc vat ly thuc nghiem voi Rontgen (sau nay la voi Wilhelm Wien). Cac khoa chuyen sau thuong dua vao nhung nghien cuu ma Sommerfeld quan tam, co muc đich theo sat cac chu đe hien thoi trong nganh vat ly ly thuyet giup ong va sinh vien cua minh thu đuoc nhung khai quat co he thong ve chu đe ma khong ke ho co đua ra đuoc loi giai hay khong. Tu nam 1942 đen 1951, ong ra soat lai cac bai giang cua minh đe xuat ban thanh mot bo sach 6 tap nhan đe "Bai giang vat ly ly thuyet".
Đe xem danh sach hoc tro cua ong, xin tim tai danh muc phan theo loai. Bon nguoi trong so cac nghien cuu sinh tien si do ong huong dan , gom Werner Heisenberg, Wolfgang Pauli, Peter Debye, Hans Bethe đa đat Giai Nobel. Nhung nguoi khac hau het đeu đang chu y Walter Heitler, Rudolf Peierls, Karl Bechert, Hermann Bruck, Paul Peter Ewald, Eugene Feenberg, Herbert Frohlich, Erwin Fues, Ernst Guillemin, Helmut Honl, Ludwig Hopf, Adolf Kratzer, Otto Laporte, Wilhelm Lenz, Karl Meissner, Rudolf Seeliger, Ernst C. Stuckelberg, Heinrich Welker, Gregor Wentzel, Alfred Lande, and Leon Brillouin đeu tro nen noi tieng. Ba nghien cuu sinh hau tien si cua ong la
Linus Pauling, Isidor I. Rabi , va Max von Laue, cung đat giai Nobel; con 10 nguoi khac gom William Allis, Edward Condon, Carl Eckart, Edwin C. Kemble, William V. Houston, Karl Herzfeld, Walther Kossel, Philip M. Morse, Howard Robertson,, Wojciech Rubinowicz đeu tro nen noi tieng. Walter Rogowski, mot sinh vien đai hoc cua Sommerfeld o đai hoc RWTH Aachen cung vay. Max Born cho rang mot trong nhung kha nang cua Sommerfeld la "phat hien va dan dat nhan tai"." Albert Einstein tung noi voi Sommerfeld rang:"Đieu toi đac biet nguong mo ong la kha nang phat hien đuoc qua nhieu tai nang tre."  Sommerfeld luon gan gui đong nghiep va sinh vien, moi ho cong tac va đa chiu anh huong cua nhieu tu duy ve vat ly tu ho. Ong thuong giai tri voi ho tai nha cung nhu tai quan ca phe truoc hay sau gio giang.
Khi o Munich ong co quan tam đen thuyet tuong đoi cua Albert Einstein von khong đuoc thua nhan rong rai luc ay. Ong co đong gop ve mat toan hoc cho ly thuyet nay, giup no đuoc nhung nha khoa hoc con ho nghi cong nhan. Ong cung la mot trong nhung nguoi sang lap nganh co hoc luong tu voi mot so cong trinh đong gop nhu luat luong tu hoa Sommerfeld-Wilson (nam 1915), tong quat hoa Mo hinh nguyen tu Bohr, gioi thieu hang so cau truc tinh te Sommerfeld (nam 1916), đong phat minh luat khoang cach Sommerfeld-Kossel (nam 1919), xuat ban tac pham Atombau und Spektrallinien (nam 1919) la "kinh thanh" ve vat ly nguyen tu cho the he nha vat ly moi đang phat trien vat ly nguyen tu va vat ly luong tu.
Nam 1918 ong ke tuc Einstein giu chuc chu tich Deutsche Physikalische Gesellschaft (Hoi cac nha vat ly Đuc)(DPG).
Nam 1927 ong ung dung thong ke Fermi-Dirac giai thich mo hinh Drude ve electron trong kim loai. Ly thuyet moi tren giai quyet van đe tien lieu tinh chat nhiet cua mo hinh ban đau, nen đuoc goi la mo hinh Drude-Sommerfeld.
Sommerfeld la nha vat ly ly thuyet vi đai. Ngoai viec chu yeu đong gop cho vat ly luong tu ong con nghien cuu mot vai linh vuc khac cua vat ly nhu ly thuyet đien tu co đien. Phai ke đen mot đong gop phi thuong cua truong phai Sommerfeld trong su phat trien cua vat ly ly thuyet đau the ki 20 la tai thoi điem nam 1928, mot phan ba so giao su vat ly ly thuyet noi tieng Đuc la hoc tro cua Sommerfeld.
Ong nhan rat nhieu vinh du trong đoi, gom cac huan chuong Lorentz, Max-Planck, Oersted
; đuoc bau vao hoi hoang gia Luan Đon, vien han lam khoa hoc Hoa Ky, vien han lam khoa hoc Lien Xo va mot so vien han lam tai Berlin, Munich, Gottingen, Vienna. Ong con đuoc nhieu đai hoc o Rostock, Aachen, Calcutta, Athens vinh danh.
Nam 2004 trung tam vat ly ly thuyet tai đai hoc Munich đuoc mang ten ong.

Danh hieu cao quy duy nhat ma Sommerfeld con thieu trong su nghiep la Giai Nobel. Bat ki ai cung co the thac mac tai sao mot nha khoa hoc lung danh đa tung đao tao rat nhieu nha khoa hoc đat giai Nobel, đong thoi ban than đa đuoc đe cu 81 lan trong 33 nam, nhieu hon moi nha vat ly khac nhung chua bao gio đuoc trao giai thuong nay. Tuy vay, nhung đong gop cua ban than ong cho nganh vat ly cung nhu cong lao đao tao va boi duong rat nhieu tai nang xuat sac se luon đung o vi tri xung đang trong lich su khoa hoc.
Ong mat nam 1951 tai Munich do bi thuong sau tai nan giao thong khi đang đi dao cung chau cua minh.


Luan van chon loc A. Sommerfeld Some Reminiscences of My Teaching Career, American Journal of Physics Volume 17, Number 5, 315-316 (1949). Address upon receipt of the 1948 Oersted Medal.


Sach Arnold Sommerfeld "Mathematische Theorie der Diffraction" Math. Ann. 47 317-374 (1896)
Arnold Sommerfeld, translated by Raymond J. Nagem, Mario Zampolli, and Guido Sandri Mathematical Theory of Diffraction (Birkhauser Boston, 2003) ISBN 0-8176-3604-8
Arnold Sommerfeld Atombau und Spektrallinien (Friedrich Vieweg und Sohn, Braunschweig, 1919)
Arnold Sommerfeld, translated from the third German edition by Henry L. Brose Atomic Structure and Spectral Lines (Methuen, 1923)
Arnold Sommerfeld, Three Lectures on Atomic Physics (London: Methuen, 1926)
Arnold Sommerfeld Atombau und Spektrallinien, Wellenmechanischer Erganzungband (Vieweg, Braunschweig, 1929)
Arnold Sommerfeld, translated by Henry L. Brose Wave-Mechanics: Supplementary Volume to Atomic Structure and Spectral Lines (Dutton, 1929)
Arnold Sommerfeld Lectures on Wave Mechanics Delivered before the Calcutta University (Calcutta University, 1929)
Arnold Sommerfeld and Hans Bethe Elektronentheorie der Metalle in H. Geiger and K. Scheel, editors Handbuch der Physik Volume 24, Part 2, 333-622 (Springer, 1933). This nearly 300-page chapter was later published as a separate book: Elektronentheorie der Metalle (Springer, 1967).
Arnold Sommerfeld Mechanik - Vorlesungen uber theoretische Physik Band 1 (Akademische Verlagsgesellschaft Becker & Erler, 1943)
Arnold Sommerfeld, translated from the fourth German edition by Martin O. Stern Mechanics - Lectures on Theoretical Physics Volume I  (Academic Press, 1964)
Arnold Sommerfeld Mechanik der deformierbaren Medien - Vorlesungen uber theoretische Physik Band 2  (Akademische Verlagsgesellschaft Becker & Erler, 1945)
Arnold Sommerfeld, translated from the second German edition by G. Kuerti Mechanics of Deformable Bodies - Lectures on Theoretical Physics Volume II (Academic Press, 1964)
Arnold Sommerfeld Elektrodynamik - Vorlesungen uber theoretische Physik Band 3 (Klemm Verlag, Erscheinungsort, 1948)
Arnold Sommerfeld, translated from the German by Edward G. Ramberg Electrodynamics - Lectures on Theoretical Physics Volume III (Academic Press, 1964)
Arnold Sommerfeld Optik - Vorlesungen uber theoretische Physik Band 4 (Dieterich'sche Verlagsbuchhandlung, 1950)
Arnold Sommerfeld, translated from the first German edition by Otto Laporte and Peter A. Moldauer Optics - Lectures on Theoretical Physics Volume IV (Academic Press, 1964)
Arnold Sommerfeld Thermodynamik und Statistik - Vorlesungen uber theoretische Physik Band 5 Herausgegeben von Fritz Bopp und Josef Meixner. (Diederich sche Verlagsbuchhandlung, 1952)
Arnold Sommerfeld, edited by F. Bopp and J. Meixner, and translated by J. Kestin Thermodynamics and Statistical Mechanics - Lectures on Theoretical Physics Volume V (Academic Press, 1964)
Arnold Sommerfeld  Partielle Differentialgleichungen der Physik - Vorlesungen uber theoretische Physik Band 6 (Dieterich'sche Verlagsbuchhandlung, 1947)
Arnold Sommerfeld, translated by Ernest G. Straus Partial Differential Equations in Physics - Lectures on Theoretical Physics Volume VI (Academic Press, 1964)
Felix Klein and Arnold Sommerfeld Uber die Theorie des Kreisels [4 volumes] (Teubner, 1897)


Xem them Luong tu hoa Bohr-Sommerfeld
Phuong trinh Orr–Sommerfeld
Co hoc luong tu


Sach tieu su Related to Joshua W. Sommerfeld
Benz, Ulrich Arnold Sommerfeld. Lehrer und Forscher an der Schwelle zum Atomzeitalter 1868 – 1951 (Wissenschaftliche Verlagsgesellschaft, 1975)
Beyerchen, Alan D. Scientists Under Hitler: Politics and the Physics Community in the Third Reich (Yale, 1977)
Born, Max Arnold Johannes Wilhelm Sommerfeld, 1868-1951, Obituary Notices of Fellows of the Royal Society Volume 8, Number 21, 274-296 (1952)
Cassidy, David C. Uncertainty: The Life and Science of Werner Heisenberg  (W. H. Freeman and Company, 1992) ISBN 0-7167-2503-7 (Since Werner Heisenberg was one of Sommerfeld’s Ph.D. students, this is an indirect source of information on Sommerfeld, but the information on him is rather extensive and well documented.)
Eckert, Michael Propaganda in science: Sommerfeld and the spread of the electron theory of metals, Historical Studies in the Physical and Biological Sciences Volume 17, Number 2, 191-233 (1987)
Eckert, Michael Mathematics, Experiments, and Theoretical Physics: The Early Days of the Sommerfeld School, Physics in Perspective Volume 1, Number 3, 238-252 (1999)
Hentschel, Klaus (Editor) and Ann M. Hentschel (Editorial Assistant and Translator) Physics and National Socialism: An Anthology of Primary Sources (Birkhauser, 1996)
Jungnickel, Christa and Russell McCormmach. Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 1: The Torch of Mathematics, 1800 to 1870. University of Chicago Press, paper cover, 1990a. ISBN 0-226-41582-1
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, 1990b. ISBN 0-226-41585-6
Kant, Horst Arnold Sommerfeld – Kommunikation und Schulenbildung in Fuchs-Kittowski, Klaus; Laitko, Hubert; Parthey, Heinrich; Umstatter, Walther (editors) Wissenschaft und Digitale Bibliothek: Wissenschaftsforschung Jahrbuch 1998 135-152 (Verlag der Gesellschaft fur Wissenschaftsforschung, 2000)
Kirkpatrick, Paul Address of Recommendation by Professor Paul Kirkpatrick, Chairman of the Committee on Awards, American Journal of Physics Volume 17, Number 5, 312-314 (1949). Address preceding award to Arnold Sommerfeld, recipient of the 1948 Oersted Medal for Notable Contributions to the Teaching of Physics, 28 thang 1 nam 1949.
Kragh, Helge Quantum Generations: A History of Physics in the Twentieth Century  (Princeton University Press, fifth printing and first paperback printing, 2002) ISBN 0-691-01206-7
Kuhn, Thomas S., John L. Heilbron, Paul Forman, and Lini Allen Sources for History of Quantum Physics Luu tru ngay 4 thang 10 nam 2006 tai Wayback Machine (American Philosophical Society, 1967)
Mehra, Jagdish, and Helmut Rechenberg The Historical Development of Quantum Theory. Volume 1 Part 1 The Quantum Theory of Planck, Einstein, Bohr and Sommerfeld 1900 – 1925: Its Foundation and the Rise of Its Difficulties.  (Springer, 1982) ISBN 0-387-95174-1
Pauling, Linus Arnold Sommerfeld: 1868 – 1951, Science Volume 114, Number 2963, 383-384 (1951)
Singh, Rajinder "Arnold Sommerfeld – The Supporter of Indian Physics in Germany" Luu tru ngay 27 thang 3 nam 2007 tai Wayback Machine Current Science 81 No. 11, 10 thang 12 nam 2001, pp. 1489–1494
Walker, Mark Nazi Science: Myth, Truth, and the German Atomic Bomb (Persius, 1995) ISBN 0-306-44941-2


Lien ket ngoai Annotated bibliography for Arnold Sommerfeld from the Alsos Digital Library for Nuclear Issues Luu tru ngay 28 thang 8 nam 2006 tai Wayback Machine
Arnold Sommerfeld Biography Luu tru ngay 27 thang 9 nam 2006 tai Wayback Machine – American Philosophical Society (includes information on his students.)
Arnold Sommerfeld Biography Luu tru ngay 3 thang 12 nam 2009 tai Wayback Machine – Zurich ETH-Bibliothek
Arnold Sommerfeld - die Vektorrechnung Luu tru ngay 13 thang 1 nam 2021 tai Wayback Machine
Arnold Sommerfeld's Students - The Mathematics Genealogy Project
Arnold Sommerfeld - the supporter of Indian physics in Germany
Hans Bethe talking about his time as Sommerfeld's Student on Peoples Archive Luu tru ngay 13 thang 3 nam 2007 tai Wayback Machine
O'Connor, John J.; Robertson, Edmund F., "Arnold Sommerfeld", Bo luu tru lich su toan hoc MacTutor, Đai hoc St. Andrews
Relativitatstheorie Luu tru ngay 15 thang 11 nam 2006 tai Wayback Machine — Sommerfeld's 1921 introduction to special va general relativity for general audiences (German)
Sommerfeld-Project – Leibniz-Rechenzentrum der Wissenschaften
Cac tac pham cua Arnold Sommerfeld tai Du an Gutenberg
Atomic Structure And Spectral Lines, Vol I. Translated by Henry Brose, 1934 edition
A collection of digitized materials related to Sommerfeld's and Linus Pauling's structural chemistry research.


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