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Complementarity (physics)
In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory. The complementarity principle holds that objects have certain pairs of complementary properties which cannot all be observed or measured simultaneously. An example of such a pair is position and momentum. Bohr considered one of the foundational truths of quantum mechanics to be the fact that setting up an experiment to measure one quantity of a pair, for instance the position of an electron, excludes the possibility of measuring the other, yet understanding both experiments is necessary to characterize the object under study. In Bohr's view, the behavior of atomic and subatomic objects cannot be separated from the measuring instruments that create the context in which the measured objects behave. Consequently, there is no "single picture" that unifies the results obtained in these different experimental contexts, and only the "totality of the pheno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves ( wave–particle duality); and there ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Podolsky
Boris Yakovlevich Podolsky (russian: link=no, Бори́с Я́ковлевич Подо́льский; June 29, 1896 – November 28, 1966) was a Russian-American physicist of Jewish descent, noted for his work with Albert Einstein and Nathan Rosen on entangled wave functions and the EPR paradox. Education In 1896, Boris Podolsky was born into a poor Jewish family in Taganrog, in the Don Host Oblast of the Russian Empire. Attended Taganrog Gymnasium. He moved to the United States in 1913. After receiving a Bachelor of Science degree in Electrical Engineering from the University of Southern California in 1918, he served in the US Army and then worked at the Los Angeles Bureau of Power and Light. In 1926, he obtained an MS in Mathematics from the University of Southern California. In 1928, he received a PhD in Theoretical Physics (under Paul Sophus Epstein) from Caltech. Career Under a National Research Council Fellowship, Podolsky spent a year at the University of Cali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copenhagen Interpretation
The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, principally attributed to Niels Bohr and Werner Heisenberg. It is one of the oldest of numerous proposed interpretations of quantum mechanics, as features of it date to the development of quantum mechanics during 1925–1927, and it remains one of the most commonly taught. There is no definitive historical statement of what the Copenhagen interpretation is. There are some fundamental agreements and disagreements between the views of Bohr and Heisenberg. For example, Heisenberg emphasized a sharp "cut" between the observer (or the instrument) and the system being observed, while Bohr offered an interpretation that is independent of a subjective observer or measurement or collapse, which relies on an "irreversible" or effectively irreversible process, which could take place within the quantum system. Features common to Copenhagen-type interpretations include the idea that quantum mechan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert Space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that defines a distance function for which the space is a complete metric space. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer), and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the term ''Hilbert space'' for the abstract concept that u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutually Unbiased Bases
In quantum information theory, mutually unbiased bases in Hilbert space C''d'' are two orthonormal bases \ and \ such that the square of the magnitude of the inner product between any basis states , e_j\rangle and , f_k\rangle equals the inverse of the dimension ''d'': : , \langle e_j, f_k \rangle, ^2 = \frac, \quad \forall j,k \in \. These bases are ''unbiased'' in the following sense: if a system is prepared in a state belonging to one of the bases, then all outcomes of the measurement with respect to the other basis are predicted to occur with equal probability. Overview The notion of mutually unbiased bases was first introduced by Schwinger in 1960, and the first person to consider applications of mutually unbiased bases was Ivanovic in the problem of quantum state determination. Another area where mutually unbiased bases can be applied is quantum key distribution, more specifically in secure quantum key exchange.M. Planat et al, A Survey of Finite Algebraic Geometrical S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pauli Matrices
In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (), they are occasionally denoted by tau () when used in connection with isospin symmetries. \begin \sigma_1 = \sigma_\mathrm &= \begin 0&1\\ 1&0 \end \\ \sigma_2 = \sigma_\mathrm &= \begin 0& -i \\ i&0 \end \\ \sigma_3 = \sigma_\mathrm &= \begin 1&0\\ 0&-1 \end \\ \end These matrices are named after the physicist Wolfgang Pauli. In quantum mechanics, they occur in the Pauli equation which takes into account the interaction of the spin of a particle with an external electromagnetic field. They also represent the interaction states of two polarization filters for horizontal/vertical polarization, 45 degree polarization (right/left), and circular polarization (right/left). Each Pauli matrix is Hermitian, and together with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin (physics)
Spin is a conserved quantity carried by elementary particles, and thus by composite particles (hadrons) and atomic nuclei. Spin is one of two types of angular momentum in quantum mechanics, the other being ''orbital angular momentum''. The orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wavefunction as the angle varies. For photons, spin is the quantum-mechanical counterpart of the polarization of light; for electrons, the spin has no classical counterpart. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The existence of the electron spin can also be inferred theoretically from the spin–statistics theorem and from the Pauli exclusion principle—and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Commutation Relation
In quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the Fourier transform of another). For example, hat x,\hat p_x= i\hbar \mathbb between the position operator and momentum operator in the direction of a point particle in one dimension, where is the commutator of and , is the imaginary unit, and is the reduced Planck's constant , and \mathbb is the unit operator. In general, position and momentum are vectors of operators and their commutation relation between different components of position and momentum can be expressed as hat r_i,\hat p_j= i\hbar \delta_ \mathbb. where \delta_ is the Kronecker delta. This relation is attributed to Werner Heisenberg, Max Born and Pascual Jordan (1925), who called it a "quantum condition" serving as a postulate of the theory; it was noted by E. Kennard (1927) to imply the Heisenberg uncertainty princip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutator (physics)
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, and , of a group , is the element : . This element is equal to the group's identity if and only if and commute (from the definition , being equal to the identity if and only if ). The set of all commutators of a group is not in general closed under the group operation, but the subgroup of ''G'' generated by all commutators is closed and is called the ''derived group'' or the ''commutator subgroup'' of ''G''. Commutators are used to define nilpotent and solvable groups and the largest abelian quotient group. The definition of the commutator above is used throughout this article, but many other group theorists define the commutator as :. Identities (group theory) Commutator identities are an important tool in group theory. The e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Observable (physics)
In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum physics, it is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value. Physically meaningful observables must also satisfy transformation laws that relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations that preserve certain mathematical properties of the space in question. Quantum mechanics In quantum physics, observables manifest as linear operators on a Hilbert space representing the state space of quantum sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Léon Rosenfeld
Léon Rosenfeld (; 14 August 1904 in Charleroi – 23 March 1974) was a Belgian physicist and Marxist. Rosenfeld was born into a secular Jewish family. He was a polyglot who knew eight or nine languages and was fluent in at least five of them. Rosenfeld obtained a PhD at the University of Liège in 1926, and he was a close collaborator of the physicist Niels Bohr. He did early work in quantum electrodynamics that predates by two decades the work by Paul Dirac and Peter Bergmann. Rosenfeld contributed to a wide range of physics fields, from statistical physics and quantum field theory to astrophysics. Along with Frederik Belinfante, he derived the Belinfante–Rosenfeld stress–energy tensor. He also founded the journal ''Nuclear Physics'' and coined the term lepton. In 1933, Rosenfeld married Yvonne Cambresier, who was one of the first women to obtain a Physics PhD from a European university. They had a daughter, Andrée Rosenfeld (1934–2008) and a son, Jean Rosenfeld. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Festschrift
In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the honoree's colleagues, former pupils, and friends. ''Festschriften'' are often titled something like ''Essays in Honour of...'' or ''Essays Presented to... .'' Terminology The term, borrowed from German, and literally meaning 'celebration writing' (cognate with ''feast-script''), might be translated as "celebration publication" or "celebratory (piece of) writing". An alternative Latin term is (literally: 'book of friends'). A comparable book presented posthumously is sometimes called a (, 'memorial publication'), but this term is much rarer in English. A ''Festschrift'' compiled and published by electronic means on the internet is called a (pronounced either or ), a term coined by the editors of the late Boris Marshak's , ''Eran ud Aner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
