Matematik fizika

Matematik fizika - fizika masalalariga qo'llash uchun matematik usullarni ishlab chiqishni anglatadi. Journal of Mathematical Physics jurnali ushbu sohani "fizika muammolariga matematikani qo'llash va bunday qo'llashlarga mos keladigan matematik usullarni ishlab chiqish va fizik nazariyalarni shakllantirish" deb ta'riflaydi. Yana bir muqobil ta'rif fizikadan ilhomlangan matematikani ham o'z ichiga oladi (shuningdek, fizik matematika deb ham ataladi). Matematik fizika - fizik jarayonlarning matematik modellari nazariyasi. Matematik fizikada asosan, nazariy fizikada qurilgan modellar matematik usullar bilan oʻrganiladi. Matematik fizika matematikada, fizikada va ularning birla-shuvi bilan alohida oʻrin egallaydi. Matematik fizika usullari fizikaning matematik modellash nazariyasi sifatida da-stlab I. Nyuton asarlarida rivojlangan. Keyinchalik Matematik fizika usullari J. Lagranj, L. Eyler, J. Furye, K. Gauss, B. Riman, M. V. Ostrogradskiylar nomi bilan bogʻliq. Oʻtgan ayerning 2-yarmidan boshlab fizik maydonlar, elektrodinamikada, akustikada, elastiklik nazariyasida, gidro- va aerodinamikada va tutash muhitlar mexanikasida vujudga keluvchi matematik modellarni oʻrganish keskin rivojlandi. Bunday fizik jarayonlarni ifodalovchi modellarni matematik usullar bilan hal qilish — xususiy hosilali differensial tenglamalar yoki Matematik fizika tenglamalari nazariyasiga tayanib amalga oshiriladi. Shu bilan birga Matematik fizika muammolarini hal qilishda differensial tenglamalardan tashqari, integral yoki integrodifferensial tenglamalar, variatsion, ehtimollar nazariyasi usullari, potensiallar nazariyasi, kompleks funksiyalar nazariyasi usullari, EHM va matematikaning boshqa boʻlimlaridan foydalaniladi.

Matematik fizikaga misol: kvant garmonik osilatorlar uchun Shredinger tenglamasining yechimlari (chapda) va ularning amplitudalari bilan (o'ngda).

20-asrda matematik fizikaga koʻzga koʻringan hissa qoʻshgan olimlar roʻyxati

20-asrning matematik fizikasiga koʻzga koʻringan hissa qoʻshgan olimlar (tugʻilgan sanasi boʻyicha):

• Uilyam Tomson (Lord Kelvin) [1824-1907]
• Oliver Heavisayd [1850–1925]
• Jyul Anri Puankare [1854-1912]
• Devid Xilbert (1862-1943)
• Arnold Sommerfeld [1868-1951]
• Konstantin Karateodori [1873-1950]
• Albert Eynshteyn [1879-1955]
• Maks tug'ilgan [1882-1970]
• Jorj Devid Birxoff [1884-1944]
• Hermann Veyl [1885-1955]
• Satyendra Nath Bose [1894-1974]
• Norbert Wiener [1894-1964]
• Jon Lighton Synge [1897-1995]
• Mario Shenberg [1914-1990]
• Volfgang Pauli [1900-1958]
• Pol Dirak [1902-1984]
• Eugene Wigner [1902-1995]
• Andrey Kolmogorov (1903-1987)
• Lars Onsager [1903-1976]
• Jon von Neumann [1903-1957]
• Sin-Itiro Tomonaga [1906-1979]
• Xideki Yukava [1907-1981]
• Nikolay Nikolaevich Bogolyubov [1909-1992]
• Subrahmanyan Chandrasekhar [1910-1995]
• Mark Kac [1914-1984]
• Julian Shvinger (1918-1994)
• Richard Phillips Feynman [1918-1988]
• Irving Ezra Segal [1918-1998]
• Ryogo Kubo [1920–1995]
• Artur Strong Wightman [1922-2013]
• Chen-Ning Yang [1922–]
• Rudolf Xaag [1922–2016]
• Friman Jon Dayson [1923–2020]
• Martin Gutsviller [1925-2014]
• Abdus Salam (1926-1996)
• Yurgen Mozer [1928-1999]
• Maykl Frensis Atiyah [1929–2019]
• Joel Louis Lebowitz [1930-]
• Rojer Penrouz [1931–]
• Elliot Hershel Lieb [1932-]
• Yakir Aharonov [1932–]
• Sheldon Glashow [1932-]
• Stiven Vaynberg [1933–2021]
• Lyudvig Dmitrievich Faddeev [1934-2017]
• Devid Ruelle [1935-]
• Yakov Grigorevich Sinay [1935-]
• Vladimir Igorevich Arnold (1937-2010)
• Artur Maykl Jaffe [1937-]
• Rim Vladimir Jekiv [1939-]
• Leonard Sasskind [1940-]
• Rodni Jeyms Baxter [1940-]
• Maykl Viktor Berri [1941-]
• Jovanni Gallavotti [1941–]
• Stiven Uilyam Xoking [1942–2018]
• Jerrold Eldon Marsden [1942–2010]
• Maykl C. Rid [1942–]
• Jon Maykl Kosterlitz [1943-]
• Isroil Maykl Sigal [1945-]
• Aleksandr Markovich Polyakov [1945-]
• Barri Saymon [1946-]
• Gerbert Spohn [1946-]
• Jon Lourens Kardi [1947-]
• Giorgio Parisi [1948-]
• Abhay Ashtekar [1949-]
• Edvard Vitten [1951-]
• F. Duncan Haldane [1951– ]
• Ashoke Sen [1956-]
• Xuan Martin Maldacena [1968–]

Shuningdek qarang

• Xalqaro matematika fizikasi assotsiatsiyasi
• Matematik fizika bo'yicha mashhur nashrlar
• Matematik fizika jurnallari ro'yxati
• O'lchov nazariyasi (matematika)
• Matematika va fizika o'rtasidagi bog'liqlik
• Nazariy, hisoblash va falsafiy fizika

Adabiyotlar

• Zaslow, Eric (2005), Physmatics, arXiv:physics/0506153, Bibcode:2005physics...6153Z

Qo'shimcha o'qish

Umumiy ishlar

• Allen, Jont (2020), An Invitation to Mathematical Physics and its History, Springer, ISBN 978-3-030-53758-6
• Courant, Richard; Hilbert, David (1989), Methods of Mathematical Physics, Vol 1–2, Interscience Publishers
• Françoise, Jean P.; Naber, Gregory L.; Tsun, Tsou S. (2006), Encyclopedia of Mathematical Physics, Elsevier, ISBN 978-0-1251-2660-1
• Joos, Georg; Freeman, Ira M. (1987), Theoretical Physics (3rd-nashr), Dover Publications, ISBN 0-486-65227-0
• Kato, Tosio (1995), Perturbation Theory for Linear Operators (2nd-nashr), Springer-Verlag, ISBN 3-540-58661-X
• Margenau, Henry; Murphy, George M. (2009), The Mathematics of Physics and Chemistry (2nd-nashr), Young Press, ISBN 978-1444627473
• Masani, Pesi R. (1976–1986), Norbert Wiener: Collected Works with Commentaries, Vol 1–4, The MIT Press
• Morse, Philip M.; Feshbach, Herman (1999), Methods of Theoretical Physics, Vol 1–2, McGraw Hill, ISBN 0-07-043316-X
• Thirring, Walter E. (1978–1983), A Course in Mathematical Physics, Vol 1–4, Springer-Verlag
• Tikhomirov, Vladimir M. (1991–1993), Selected Works of A. N. Kolmogorov, Vol 1–3, Kluwer Academic Publishers
• Titchmarsh, Edward C. (1985), The Theory of Functions (2nd-nashr), Oxford University Press

Bakalavr bosqichi uchun darsliklar

• Arfken, George B.; Weber, Hans J.; Harris, Frank E. (2013), Mathematical Methods for Physicists: A Comprehensive Guide (7th-nashr), Academic Press, ISBN 978-0-12-384654-9, (Mathematical Methods for Physicists, Solutions for Mathematical Methods for Physicists (7th ed.), archive.org)
• Bayın, Selçuk Ş. (2018), Mathematical Methods in Science and Engineering (2nd-nashr), Wiley, ISBN 9781119425397
• Boas, Mary L. (2006), Mathematical Methods in the Physical Sciences (3rd-nashr), Wiley, ISBN 978-0-471-19826-0
• Butkov, Eugene (1968), Mathematical Physics, Addison-Wesley
• Hassani, Sadri (2009), Mathematical Methods for Students of Physics and Related Fields, (2nd ed.), New York, Springer, eISBN 978-0-387-09504-2
• Jeffreys, Harold; Swirles Jeffreys, Bertha (1956), Methods of Mathematical Physics (3rd-nashr), Cambridge University Press
• Marsh, Adam (2018), Mathematics for Physics: An Illustrated Handbook, World Scientific, ISBN 978-981-3233-91-1
• Mathews, Jon; Walker, Robert L. (1970), Mathematical Methods of Physics (2nd-nashr), W. A. Benjamin, ISBN 0-8053-7002-1
• Menzel, Donald H. (1961), Mathematical Physics, Dover Publications, ISBN 0-486-60056-4
• Riley, Ken F.; Hobson, Michael P.; Bence, Stephen J. (2006), Mathematical Methods for Physics and Engineering (3rd-nashr), Cambridge University Press, ISBN 978-0-521-86153-3
• Stakgold, Ivar (2000), Boundary Value Problems of Mathematical Physics, Vol 1-2., Society for Industrial and Applied Mathematics, ISBN 0-89871-456-7
• Starkovich, Steven P. (2021), The Structures of Mathematical Physics: An Introduction, Springer, ISBN 978-3-030-73448-0

Magistratura uchun darsliklar

• Blanchard, Philippe; Brüning, Erwin (2015), Mathematical Methods in Physics: Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics (2nd-nashr), Springer, ISBN 978-3-319-14044-5
• Cahill, Kevin (2019), Physical Mathematics (2nd-nashr), Cambridge University Press, ISBN 978-1-108-47003-2
• Geroch, Robert (1985), Mathematical Physics, University of Chicago Press, ISBN 0-226-28862-5
• Hassani, Sadri (2013), Mathematical Physics: A Modern Introduction to its Foundations (2nd-nashr), Springer-Verlag, ISBN 978-3-319-01194-3
• Marathe, Kishore (2010), Topics in Physical Mathematics, Springer-Verlag, ISBN 978-1-84882-938-1
• Milstein, Grigori N.; Tretyakov, Michael V. (2021), Stochastic Numerics for Mathematical Physics (2nd-nashr), Springer, ISBN 978-3-030-82039-8
• Reed, Michael C.; Simon, Barry (1972–1981), Methods of Modern Mathematical Physics, Vol 1-4, Academic Press
• Richtmyer, Robert D. (1978–1981), Principles of Advanced Mathematical Physics, Vol 1-2., Springer-Verlag
• Rudolph, Gerd; Schmidt, Matthias (2013–2017), Differential Geometry and Mathematical Physics, Vol 1-2, Springer
• Serov, Valery (2017), Fourier Series, Fourier Transform and Their Applications to Mathematical Physics, Springer, ISBN 978-3-319-65261-0
• Simon, Barry (2015), A Comprehensive Course in Analysis, Vol 1-5, American Mathematical Society
• Stakgold, Ivar; Holst, Michael (2011), Green's Functions and Boundary Value Problems (3rd-nashr), Wiley, ISBN 978-0-470-60970-5
• Stone, Michael; Goldbart, Paul (2009), Mathematics for Physics: A Guided Tour for Graduate Students, Cambridge University Press, ISBN 978-0-521-85403-0
• Szekeres, Peter (2004), A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry, Cambridge University Press, ISBN 978-0-521-53645-5
• Taylor, Michael E. (2011), Partial Differential Equations, Vol 1-3 (2nd-nashr), Springer.
• Whittaker, Edmund T.; Watson, George N. (1950), A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions, with an Account of the Principal Transcendental Functions (4th-nashr), Cambridge University Press

Klassik fizika bo'yicha maxsus matnlar

• Abraham, Ralph; Marsden, Jerrold E. (2008), Foundations of Mechanics: A Mathematical Exposition of Classical Mechanics with an Introduction to the Qualitative Theory of Dynamical Systems (2nd-nashr), AMS Chelsea Publishing, ISBN 978-0-8218-4438-0
• Adam, John A. (2017), Rays, Waves, and Scattering: Topics in Classical Mathematical Physics, Princeton University Press., ISBN 978-0-691-14837-3
• Arnold, Vladimir I. (1997), Mathematical Methods of Classical Mechanics (2nd-nashr), Springer-Verlag, ISBN 0-387-96890-3
• Bloom, Frederick (1993), Mathematical Problems of Classical Nonlinear Electromagnetic Theory, CRC Press, ISBN 0-582-21021-6
• Boyer, Franck; Fabrie, Pierre (2013), Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models, Springer, ISBN 978-1-4614-5974-3
• Colton, David; Kress, Rainer (2013), Integral Equation Methods in Scattering Theory, Society for Industrial and Applied Mathematics, ISBN 978-1-611973-15-0
• Ciarlet, Philippe G. (1988–2000), Mathematical Elasticity, Vol 1–3, Elsevier
• Galdi, Giovanni P. (2011), An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems (2nd-nashr), Springer, ISBN 978-0-387-09619-3
• Hanson, George W.; Yakovlev, Alexander B. (2002), Operator Theory for Electromagnetics: An Introduction, Springer, ISBN 978-1-4419-2934-1
• Kirsch, Andreas; Hettlich, Frank (2015), The Mathematical Theory of Time-Harmonic Maxwell's Equations: Expansion-, Integral-, and Variational Methods, Springer, ISBN 978-3-319-11085-1
• Knauf, Andreas (2018), Mathematical Physics: Classical Mechanics, Springer, ISBN 978-3-662-55772-3
• Lechner, Kurt (2018), Classical Electrodynamics: A Modern Perspective, Springer, ISBN 978-3-319-91808-2
• Marsden, Jerrold E.; Ratiu, Tudor S. (1999), Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (2nd-nashr), Springer, ISBN 978-1-4419-3143-6
• Müller, Claus (1969), Foundations of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, ISBN 978-3-662-11775-0
• Ramm, Alexander G. (2018), Scattering by Obstacles and Potentials, World Scientific, ISBN 9789813220966
• Roach, Gary F.; Stratis, Ioannis G.; Yannacopoulos, Athanasios N. (2012), Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics, Princeton University Press, ISBN 978-0-691-14217-3

Zamonaviy fizika bo'yicha maxsus matnlar

• Baez, John C.; Muniain, Javier P. (1994), Gauge Fields, Knots, and Gravity, World Scientific, ISBN 981-02-2034-0
• Blank, Jiří; Exner, Pavel; Havlíček, Miloslav (2008), Hilbert Space Operators in Quantum Physics (2nd-nashr), Springer, ISBN 978-1-4020-8869-8
• Engel, Eberhard; Dreizler, Reiner M. (2011), Density Functional Theory: An Advanced Course, Springer-Verlag, ISBN 978-3-642-14089-1
• Glimm, James; Jaffe, Arthur (1987), Quantum Physics: A Functional Integral Point of View (2nd-nashr), Springer-Verlag, ISBN 0-387-96477-0
• Haag, Rudolf (1996), Local Quantum Physics: Fields, Particles, Algebras (2nd-nashr), Springer-Verlag, ISBN 3-540-61049-9
• Hall, Brian C. (2013), Quantum Theory for Mathematicians, Springer, ISBN 978-1-4614-7115-8
• Hamilton, Mark J. D. (2017), Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physics, Springer, ISBN 978-3-319-68438-3
• Hawking, Stephen W.; Ellis, George F. R. (1973), The Large Scale Structure of Space-Time, Cambridge University Press, ISBN 0-521-20016-4
• Jackiw, Roman (1995), Diverse Topics in Theoretical and Mathematical Physics, World Scientific, ISBN 9810216963
• Landsman, Klaas (2017), Foundations of Quantum Theory: From Classical Concepts to Operator Algebras, Springer, ISBN 978-3-319-51776-6
• Moretti, Valter (2017), Spectral Theory and Quantum Mechanics: Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation (2nd-nashr), Springer, ISBN 978-3-319-70705-1
• Robert, Didier; Combescure, Monique (2021), Coherent States and Applications in Mathematical Physics (2nd-nashr), Springer, ISBN 978-3-030-70844-3
• Tasaki, Hal (2020), Physics and mathematics of quantum many-body systems, Springer, ISBN 978-3-030-41265-4, OCLC 1154567924
• Teschl, Gerald (2009), Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators, American Mathematical Society, ISBN 978-0-8218-4660-5
• Thirring, Walter E. (2002), Quantum Mathematical Physics: Atoms, Molecules and Large Systems (2nd-nashr), Springer-Verlag, ISBN 978-3-642-07711-1
• von Neumann, John (2018), Mathematical Foundations of Quantum Mechanics, Princeton University Press, ISBN 978-0-691-17856-1
• Weyl, Hermann (2014), The Theory of Groups and Quantum Mechanics, Martino Fine Books, ISBN 978-1614275800
• Ynduráin, Francisco J. (2006), The Theory of Quark and Gluon Interactions (4th-nashr), Springer, ISBN 978-3642069741
• Zeidler, Eberhard (2006–2011), Quantum Field Theory: A Bridge Between Mathematicians and Physicists, Vol 1-3, Springer