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Gruppentheorie Und Quantenmechanik
''Gruppentheorie und Quantenmechanik'', or ''The Theory of Groups and Quantum Mechanics'', is a textbook written by Hermann Weyl about the mathematical study of symmetry, group theory, and how to apply it to quantum physics. Weyl expanded on ideas he published in a 1927 paper, basing the text on lectures he gave at ETH Zurich during the 1927–28 academic year. The first edition was published by in Leipzig in 1928; a second edition followed in 1931, which was translated into English by Howard P. Robertson. Dover Publications issued a reprint of this translation in 1950. John Archibald Wheeler wrote of learning quantum mechanics from Weyl's book, "His style is that of a smiling figure on horseback, cutting a clean way through, on a beautiful path, with a swift bright sword." Edward Condon called the text "authoritative". Julian Schwinger said of it, "I read and re-read that book, each time progressing a little farther, but I cannot say that I ever – not even to this day – full ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Weyl
Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well as purely mathematical disciplines such as number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years. Weyl contributed to an exceptionally wide range of fields, including works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. Freeman Dyson wrote that Weyl alone bore comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalizations Of Pauli Matrices
In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few classes of such matrices are summarized. Multi-qubit Pauli matrices (Hermitian) This method of generalizing the Pauli matrices refers to a generalization from a single 2-level system (qubit) to multiple such systems. In particular, the generalized Pauli matrices for a group of N qubits is just the set of matrices generated by all possible products of Pauli matrices on any of the qubits. The vector space of a single qubit is V_1 = \mathbb^2 and the vector space of N qubits is V_N = \left(\mathbb^2\right)^\cong \mathbb^. We use the tensor product notation :\sigma_a^ = I^ \otimes \dotsm \otimes I^ \otimes \sigma_a \otimes I^ \otimes \dotsm \otimes I^, \qquad a = 1, 2, 3 to refer to the operator on V_N that acts as a Pauli matrix on the nth qubit and the identity on a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics Textbooks
Physics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Textbooks
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1931 Non-fiction Books
Events January * January 2 – South Dakota native Ernest Lawrence invents the cyclotron, used to accelerate particles to study nuclear physics. * January 4 – German pilot Elly Beinhorn begins her flight to Africa. * January 22 – Sir Isaac Isaacs is sworn in as the first Australian-born Governor-General of Australia. * January 25 – Mohandas Gandhi is again released from imprisonment in India. * January 27 – Pierre Laval forms a government in France. * January 30 – Charlie Chaplin comedy drama film ''City Lights'' receives its public premiere at the Los Angeles Theater with Albert Einstein as guest of honor. Contrary to the current trend in cinema, it is a silent film, but with a score by Chaplin. Critically and commercially successful from the start, it will place consistently in lists of films considered the best of all time. February * February 4 – Soviet leader Joseph Stalin gives a speech calling for rapid industrialization, arguing that only strong indus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1928 Non-fiction Books
Nineteen or 19 may refer to: * 19 (number) * One of the years 19 BC, AD 19, 1919, 2019 Films * 19 (film), ''19'' (film), a 2001 Japanese film * Nineteen (1987 film), ''Nineteen'' (1987 film), a 1987 science fiction film * ''19-Nineteen'', a 2009 South Korean film * ''Diciannove'', a 2024 Italian drama film informally referred to as "Nineteen" in some sources Science * Potassium, an alkali metal * 19 Fortuna, an asteroid Music * 19 (band), a Japanese pop music duo Albums * 19 (Adele album), ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD (rapper), MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * XIX (EP), ''XIX'' (EP), a 2019 EP by 1the9 Songs * 19 (song), "19" (song), a 1985 song by British musician Paul Hardcastle * "Stone in Focus", officially "#19", a composition by Aphex Twin * "Nineteen", a song fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Mackey
George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions to quantum logic, representation theory, and noncommutative geometry. Career Mackey earned his B.A. at Rice University in 1938 and obtained his Ph.D. at Harvard University in 1942 under the direction of Marshall H. Stone. He joined the Harvard University Mathematics Department in 1943, was appointed Landon T. Clay Professor of Mathematics and Theoretical Science in 1969 and remained there until he retired in 1985. Work Earlier in his career Mackey did significant work in the duality theory of locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products. Mackey was one of the pioneer workers in the intersection of quantum logic, the theory of infinite-dimensional unitary representations of groups, the theory of operator algebras and noncommutative geometry. A central role ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including websites, Application software, software applications, music, audiovisual, and print materials. The Archive also advocates a Information wants to be free, free and open Internet. Its mission is committing to provide "universal access to all knowledge". The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hundreds of billions of web captures. The Archive also oversees numerous Internet Archive#Book collections, book digitization projects, collectively one of the world's largest book digitization efforts. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positron
The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatter counterpart) of the electron. When a positron collides with an electron, annihilation occurs. If this collision occurs at low energies, it results in the production of two or more photons. Positrons can be created by positron emission radioactive decay (through weak interactions), or by pair production from a sufficiently energetic photon which is interacting with an atom in a material. History Theory In 1928, Paul Dirac published a paper proposing that electrons can have both a positive and negative charge. This paper introduced the Dirac equation, a unification of quantum mechanics, special relativity, and the then-new concept of electron Spin (physics), spin to explain the Zeeman effect. The paper did not explicitly predict a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proton
A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an electron (the proton-to-electron mass ratio). Protons and neutrons, each with a mass of approximately one Dalton (unit), dalton, are jointly referred to as ''nucleons'' (particles present in atomic nuclei). One or more protons are present in the Atomic nucleus, nucleus of every atom. They provide the attractive electrostatic central force which binds the atomic electrons. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol ''Z''). Since each chemical element, element is identified by the number of protons in its nucleus, each element has its own atomic number, which determines the number of atomic electrons and consequently the chemical characteristi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antimatter
In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding subatomic particle, particles in "ordinary" matter, and can be thought of as matter with reversed charge and parity, or going backward in time (see CPT symmetry). Antimatter occurs in natural processes like cosmic ray collisions and some types of radioactive decay, but only a tiny fraction of these have successfully been bound together in experiments to form antiatoms. Minuscule numbers of antiparticles can be generated at particle accelerators, but total artificial production has been only a few nanograms. No Macroscopic scale, macroscopic amount of antimatter has ever been assembled due to the extreme cost and difficulty of production and handling. Nonetheless, antimatter is an essential component of widely available applications related to beta decay, such as positron emission tomography, radiation therapy, and industrial imaging. In theory, a particle and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up quark, up and down quark, down quarks. Electrons are extremely lightweight particles that orbit the positively charged atomic nucleus, nucleus of atoms. Their negative charge is balanced by the positive charge of protons in the nucleus, giving atoms their overall electric charge#Charge neutrality, neutral charge. Ordinary matter is composed of atoms, each consisting of a positively charged nucleus surrounded by a number of orbiting electrons equal to the number of protons. The configuration and energy levels of these orbiting electrons determine the chemical properties of an atom. Electrons are bound to the nucleus to different degrees. The outermost or valence electron, valence electrons are the least tightly bound and are responsible for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
