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Academic literature on the topic 'Commutation relations (Quantum mechanics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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Journal articles on the topic "Commutation relations (Quantum mechanics)"

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WIDOM, A., and Y. N. SRIVASTAVA. "QUANTUM FLUID MECHANICS AND QUANTUM ELECTRODYNAMICS." Modern Physics Letters B 04, no. 01 (January 10, 1990): 1–8. http://dx.doi.org/10.1142/s0217984990000027.

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The commutation relations of Landau quantum fluid mechanics are compared with those of quantum electrodynamics. In both cases, the operator representation of the commutators require a macroscopic phase, and a wavefunction periodic in that phase. A physical discussion is given for analogous effects in superfluids and superconductors, with regard to quantum coherence on a macroscopic scale. Other applications are then briefly described.

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SHABANOV, SERGEI V. "q-OSCILLATORS, NON-KÄHLER MANIFOLDS AND CONSTRAINED DYNAMICS." Modern Physics Letters A 10, no. 12 (April 20, 1995): 941–48. http://dx.doi.org/10.1142/s0217732395001034.

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It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kähler manifolds, or as a quantum theory with second- (or first-) class constraints.

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Man'ko, V. I., G. Marmo, F. Zaccaria, and E. C. G. Sudarshan. "Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics." International Journal of Modern Physics B 11, no. 10 (April 20, 1997): 1281–96. http://dx.doi.org/10.1142/s0217979297000666.

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It is shown that for quantum systems the vector field associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schrödinger and Heisenberg picture. We illustrate these ambiguities in terms of simple examples.

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IORIO, ALFREDO, and GIUSEPPE VITIELLO. "QUANTUM GROUPS AND VON NEUMANN THEOREM." Modern Physics Letters B 08, no. 04 (February 20, 1994): 269–76. http://dx.doi.org/10.1142/s0217984994000285.

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We discuss the q-deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in quantum mechanics. We show that the q-deformation parameter labels the Weyl systems in quantum mechanics and the unitarily inequivalent representations of the canonical commutation relations in quantum field theory.

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Shakhova, E. A., P. P. Rymkevich, A. S. Gorshkov, M. Y. Egorov, and A. S. Stepashkina. "Energy processes with natural quantization." E3S Web of Conferences 124 (2019): 01046. http://dx.doi.org/10.1051/e3sconf/201912401046.

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The paper shows that the quantum-mechanical approach is applicable to most macro processes occurring in nature include the power industry. The mathematical apparatus of the isomorphic Heisenberg algebra is proposed. A non-commutative ring is constructed within which the commutation relations are given. The transition from quantum to classical theory is shown.

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PEDRAM, POURIA. "A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS." International Journal of Modern Physics D 19, no. 12 (October 2010): 2003–9. http://dx.doi.org/10.1142/s0218271810018153.

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Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

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Kober, Martin. "Quaternionic quantization principle in general relativity and supergravity." International Journal of Modern Physics A 31, no. 04n05 (February 3, 2016): 1650004. http://dx.doi.org/10.1142/s0217751x16500044.

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A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space–time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to [Formula: see text] supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.

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FLORATOS, EMMANUEL. "MATRIX QUANTIZATION OF TURBULENCE." International Journal of Bifurcation and Chaos 22, no. 09 (September 2012): 1250213. http://dx.doi.org/10.1142/s0218127412502136.

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Based on our recent work on Quantum Nambu Mechanics [Axenides & Floratos 2009], we provide an explicit quantization of the Lorenz chaotic attractor through the introduction of noncommutative phase space coordinates as Hermitian N × N matrices in R3. For the volume preserving part, they satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction, it violates the quantum commutation relations. We demonstrate that the Heisenberg–Nambu evolution equations for the Matrix Lorenz system develop fast decoherence to N independent Lorenz attractors. On the other hand, there is a weak dissipation regime, where the quantum mechanical properties of the volume preserving nondissipative sector survive for long times.

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Brooke, J. A., and E. Prugovečki. "Relativistic canonical commutation relations and the geometrization of quantum mechanics." Il Nuovo Cimento A 89, no. 2 (September 1985): 126–48. http://dx.doi.org/10.1007/bf02804855.

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Chester, David, Xerxes D. Arsiwalla, Louis H. Kauffman, Michel Planat, and Klee Irwin. "Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density." Symmetry 16, no. 3 (March 6, 2024): 316. http://dx.doi.org/10.3390/sym16030316.

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We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman–von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize spacetime, energy–momentum, frequency–wavenumber, and the Fourier conjugate of energy–momentum. We clarify how first and second quantization can be found by simply mapping between operators in classical and quantum commutator algebras.

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Dissertations / Theses on the topic "Commutation relations (Quantum mechanics)"

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Kleeman, R. "Generalized quantization and colour algebras /." Title page, table of contents and abstract only, 1985. http://web4.library.adelaide.edu.au/theses/09PH/09phk635.pdf.

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Rosaler, Joshua S. "Inter-theory relations in physics : case studies from quantum mechanics and quantum field theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:1fc6c67d-8c8e-4e92-a9ee-41eeae80e145.

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I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level (purportedly more accurate and encompassing) model to that of the high-level (purportedly less accurate and encompassing) model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.

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Waters, Jayson Cydhaarth. "Estranged/Entangled: The History, Theory, and Technology of Quantum Mechanics in International Relations." Thesis, The University of Sydney, 2022. https://hdl.handle.net/2123/29604.

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In recent years a growing number of scholars of international relations (IR) have looked hopefully towards quantum mechanics (QM) as a source of new analytical tools and critical approaches to address many of the intractable problems — and emergent challenges — faced by the discipline and the world. It now appears that what some call a new ‘wave’ — or ‘turn’ or ‘era’ — and others a paradigm shift may be coming to the discipline. Novel, and more accurate, methods for modelling behaviour are being introduced by Quantum Decision Theory and Quantum Game Theory, and old Newtonian analogies, metaphors, and cosmologies are being challenged and replaced by quantum equivalents. Alexander Wendt has even gone so far as to suggest that scholars need to rethink the social sciences from the (quantum) mind up. In place of traditional mind/body dualism, Wendt proposes a quantum monism based on a panpsychist quantum theory of mind. This is a radical proposal, the ramifications of which could drastically reframe understandings of both the social and physical aspects of the world. While there is no doubt that the present ‘quantum wave’ in IR is the most significant, it is not the first. In 1927, during his address to the American Political Science Association, William Bennett Munro called for political scientists to engage with QM and to borrow, by analogy, from the ‘new physics’ to “get rid of intellectual insincerities concerning the nature of sovereignty, the general will, natural rights, and the freedom of the individual” and discover “the true purposes and policies which should direct human action in matters of government.” Remarkably, Munro’s appeal came a mere two months after Max Born and Werner Heisenberg declared “quantum mechanics to be a closed theory” at the Fifth Solvay Conference. Some headway was made during the interwar period, but a complex combination of circumstances leading up to, and following, the Second World War estranged this line of scientific inquiry from IR theory. This pattern of estrangement and entanglement has recurred several times in the history of IR. This thesis employs an experimental methodology to interrogate three neglected aspects of the relationship between QM and IR. The critical approaches of genealogy, semiology, and dromology are applied, respectively, to the historical, theoretical, and technological entanglements of IR and QM. Reinterpreting nearly a century of estrangement and entanglement, the thesis makes the case for a quantum theory of IR that is process-relational and event-ontological. Ultimately, however, this thesis is a work of pre-theory. Rather than presenting a critique of quantum IR, or an attempt at a fully formed quantum theory of IR, this thesis lays the groundwork for future theory and future developments in quantum IR.

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Mickelin, Oscar. "On Spectral Inequalities in Quantum Mechanics and Conformal Field Theory." Thesis, KTH, Matematik (Avd.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-167969.

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Following Exner et al. (Commun. Math. Phys. 26 (2014), no. 2, 531–541), we prove new Lieb-Thirring inequalities for a general class of self-adjoint, second order differential operators with matrix-valued potentials, acting in one space-dimension. This class contains, but is not restricted to, the magnetic and non-magnetic Schrödinger operators. We consider the three cases of functions defined on all reals, all positive reals, and an interval, respectively, and acquire three different kinds of bounds. We also investigate the spectral properties of a family of operators from conformal field theory, by proving an asymptotic phase-space bound on the eigenvalue counting function and establishing a number of spectral inequalities. These bound the Riesz-means of eigenvalues for these operators, together with each individual eigenvalue, and are applied to a few physically interesting examples.
Vi följer Exner et al. (Commun. Math. Phys. 26 (2014), nr. 2, 531–541) och bevisar nya Lieb-Thirring-olikheter för generella, andra gradens självadjungerade differentialoperatorer med matrisvärda potentialfunktioner, verkandes i en rumsdimension. Dessa innefattar och generaliserar de magnetiska och icke-magnetiska Schrödingeroperatorerna. Vi betraktar tre olika fall, med funktioner definierade på hela reella axeln, på den positiva reella axeln, samt på ett interval. Detta resulterar i tre sorters olikheter. Vidare undersöker vi spektralegenskaperna för en klass operatorer från konform fältteori, genom att asymptotiskt begränsa antalet egenvärden med ett fasrymdsuttryck, samt genom att bevisa ett antal spektralolikheter. Dessa begränsar Riesz-medelvärdena för operatorerna, samt varje enskilt egenvärde, och tillämpas på ett par fysikaliskt intressanta exempel.

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Nazaikinskii, Vladimir, Bert-Wolfgang Schulze, and Boris Sternin. "Quantization methods in differential equations : Chapter 2: Exactly soluble commutation relations (The simplest class of classical mechanics)." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2579/.

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Alecce, Antonio. "Selected problems in quantum mechanics: towards topological quantum devices and heat engine." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3421931.

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The work presented in this thesis meanly addresses two topics in theoretical physics which are quantum thermodynamics and topological order. In the first case, physicists are trying to build up a theory able to describe quite in general phenomena involving heat and energy exchanges in quantum systems. The second topic, instead, is related to exotic phenomena and states of matter like the quantum Hall effect (QHE) or topological insulators and topological superconductors. In the first part od the thesis we define the quantum dynamics for closed and open systems. This is a key ingredient to address the field of quantum thermodynamics. Then, after an introductory part about the quantum thermodynamic transformations, we move toward the field of nonequilibrium fluctuation relations. We address the problem of irreversibility in classical as well as quantum mechanics. Here we present one of our main result. We characterize the "thermodynamic" irreversible adiabatic evolution of a quantum system starting such branch in a thermal equilibrium state at inverse temperature ßi. We give the amount of thermodynamic entropy growth for the process. As direct application of the preceding result we then address a quantum Otto cycle (QOC) working at finite power. We saw that the increasing of irreversible character of the evolution affects the main figures of merit of the cycle. The second part of the thesis addresses the field of topological order. At first we introduce the concept of topological orders, classes and invariants. Then we introduce the well known Kitaev model for 1 D superconductors. This model predicts Majorana zero mode at the ends of the wire (the 1 D system). MZM are topological states showing great resistance against disorder, local perturbations and any dissipative element. Then we consider a generalized Kitaev model where long range interactions are accounted. We get rich topological phase diagrams showing the presence of several MZM per edge. We study the appearing/disappearing dynamics of the modes according to the time reversal symmetry, that is fundamental in the study of topological phase. The phase diagrams we obtained also show the presence of massive edge modes. In this last case the topological invariants do not well describe any transition. At last we focused on a very limit cases where MZM are obtained at finite length of the wire. Such cases are really interesting since the great advance we can get from the finiteness of the wire in an experimental setup. The last part is about single electron tunneling devices. Here we got a different ability to work as "heat-to-current harvester" for a device using quantum dots respect to an analogue one using metallic dots. These different arguments find their unity by considering recent scientific works in which heat transport is addressed in single electron transistor devices where some element of the circuit shows a topological behaviour. This is a perfect system from hich we can get new transport phenomena.
Il lavoro presentato in questa tesi tratta principalmente due argomenti quali le termodinamica quantistica e l'ordine topologico. Nel primo caso fisici stanno provando a costruire una teoria capace to descrivere abbastanza in generale gli scambi di calore ed energia in sistemi quantistici. Il secondo argomento, invece, si relaziona a fenomini e stati della meteria esotici come l'effetto "fractional quantum hall" o gli isolanti e superconduttori topologici. Nella prima parte della tesi definiamo la dinamica quantistica per un sistema chiuso ed aperto. Questo é fondamentale per trattare il campo della termodinamica quantistica. Poi, dopo una parte introduttiva sulle trasformazioni termodinamiche quantistiche, ci si sposta verso il campo delle relazioni di fluttuazione non all'equilibrio. Viene trattato il problema dell'irreversibilità tanto nella meccanica classica quanto in quella quantistica. Qui presentiamo uno dei nostri maggiori risultati. Caratterizziamo un'evoluzione adiabatica "termodinamica" irreversibile di un sistema quantistico il cui stato iniziale é uno di equilibrio alla temperatura inversa iniziale ßi. Viene ricavato l'incremento di entropia termodinamica del processo. Come applicazione diretta del risultato precedente si é considerato un ciclo Otto quantistico (QOC). Abbiamo notato che l'aumentare del carattere irreversibile dell'evoluzione inficia le principali figure di merito del ciclo. La seconda parte della tisi, invece, guarda al campo dell'ordine topologico. All'inizio introduciamo i concetti di ordine, classi ed invarianti topologici. Poi introduciamo il ben noto modello di Kitaev per superconduttori 1 D. Questo modello prevede "Majorana zero mode" (MZM) ai capi del filo (il sistema 1 D). I Majorana zero modes sono stati topologici che mostrano una grande resistenza contro il disordine, perurbazioni locali e ogni genere di elemento dissipativo. In viene considerata una generalizzazione del modello di Kitaev con interazioni a molti vicini. Vengono ricavati diagrammi di fase topologica molto "ricchi" che mostrano la presenza di molti MZM per lato. Inoltre si studia l'apparire e scomparire di tali modi a seconda della simmetria di inversione temporale, che é fondamentale per lo studio della fase topologica. I diagrammi di fase mostrano anche la presenza di massive edge modes. In questo ultimo caso gli invarianti topologici non descrivono bene tutte le transizioni. In fine ci siamo focalizzati sul caso limite dove gli MZM sono ottenuti quando il sistema ha una lunghezza finita. Tali casi sono molto interressanti visto il grande vantaggio che possiamo ricavarne in un setup sperimentale dato che il sistema può grandezza ridotta. L'ultima parte é sui dispositivi single electron tunneling. Qui abbiamo descritto la differente capacità a lavorare come "heat-to-current harvester" per un dispositivo che usa quantum dots rispetto ad uno analogo che usa metallic dots. Questi argomenti differenti trovano un punto di unione considerando lavori scientifici recenti in cui si considera trasporto di calore su dispositivi "single electron tuunneling" in cui alcune delle componenti circuitali dei dispositivi mostrano una natura topologica. Sono sistemi perfetti dai quali possiamo ottenere nuovi fenomeni di trasporto.

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Genovese, Fabrizio Romano. "Generalized relations for compositional models of meaning." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:3b555c2a-6067-422c-9f1b-b1a5af8053ff.

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In this thesis, tools of categorical quantum mechanics are used to explain natural language from a cognitive point of view. Categories of generalized relations are developed for the task, examples are provided, and languages that are particularly tricky to describe using this approach are taken into consideration.

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Gandhi, Sohang. "Topological Generalizations of the Heisenberg Uncertainty Relation." Honors in the Major Thesis, University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/1222.

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This item is only available in print in the UCF Libraries. If this is your Honors Thesis, you can help us make it available online for use by researchers around the world by following the instructions on the distribution consent form at http://library.ucf.edu/Systems/DigitalInitiatives/DigitalCollections/InternetDistributionConsentAgreementForm.pdf You may also contact the project coordinator, Kerri Bottorff, at kerri.bottorff@ucf.edu for more information.
Bachelors
Arts and Sciences
Physics

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Kleeman, R. (Richard). "Generalized quantization and colour algebras / by R. Kleeman." 1985. http://hdl.handle.net/2440/20597.

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Bibliography: leaves 143-146
vii, 147 leaves ; 30 cm.
Title page, contents and abstract only. The complete thesis in print form is available from the University Library.
Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematical Physics, 1986

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Hibberd, Anthony Noel. "Yang-Baxter relations in conformal field theory." Phd thesis, 2001. http://hdl.handle.net/1885/147953.

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Books on the topic "Commutation relations (Quantum mechanics)"

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Samoĭlenko, S. I. Sravnitelʹnyĭ analiz metodov kommutat͡sii dli͡a t͡sifrovykh seteĭ integralʹnogo obsluzhivanii͡a. Moskva: Akademii͡a nauk SSSR, Nauchno-tekhn. t͡sentr informat͡sionno-vychislitelʹnykh seteĭ, 1991.

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T͡Sit͡siashvili, G. Sh. Kommutat͡sionnye ėffekty v modelʹnykh fizicheskikh statistikakh. Vladivostok: In-t prikladnoĭ matematiki DVO RAN, 1993.

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Petz, Dénes. An invitation to the algebra of canonical commutation relations. Leuven (Belgium): Leuven University Press, 1990.

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D, Han, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch, eds. Third International Workshop on Squeezed States and Uncertainty Relations: Proceedings of a workshop held at the University of Maryland, Baltimore County, Baltimore, Maryland, August 10-13, 1993. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1994.

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Isaacson, Walter. Einstein: Su vida y su universo. Barcelona: Debate, 2008.

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Isaacson, Walter. Einstein: Cuộc đời và vũ trụ. Thành phố Hồ Chí Minh: Nhà xuất bản Tổng Hợp TP. Hồ Chí Minh, 2011.

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Moore, R. T., and P. E. T. Jørgensen. Operator Commutation Relations: Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups. Springer, 2012.

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Petz, D., and Dbenes Petz. An Invitation to the Algebra of Canonical Commutation Relations (Leuven Notes in Mathematical and Theoretical Physics). Coronet Books, 1990.

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Horing, Norman J. Morgenstern. Schwinger Action Principle and Variational Calculus. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0004.

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Chapter 4 introduces the Schwinger Action Principle, along with associated particle and potential sources. While the methods described here originally arose in the relativistic quantum field theory of elementary particle physics, they have also profoundly advanced our understanding of non-relativistic many-particle physics. The Schwinger Action Principle is a quantum-mechanical variational principle that closely parallels the Hamilton Principle of Least Action of classical mechanics, generalizing it to include the role of quantum operators as generalized coordinates and momenta. As such, it unifies all aspects of quantum theory, incorporating Hamilton equations of motion for those operators and the Heisenberg equation, as well as producing the canonical equal-time commutation/anticommutation relations. It yields dynamical coupled field equations for the creation and annihilation operators of the interacting many-body system by variational differentiation of the Hamiltonian with respect to the field operators. Also, equations for the development of matrix elements (underlying Green’s functions) are derived using variations with respect to particle and potential “sources” (and coupling strength). Variational calculus, involving impressed potentials, c-number coordinates and fields, also quantum operator coordinates and fields, is discussed in full detail. Attention is given to the introduction of fermion and boson particle sources and their use in variational calculus.

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Arai, Asao. Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations: Representation-theoretical Viewpoint for Quantum Phenomena. Springer, 2020.

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Book chapters on the topic "Commutation relations (Quantum mechanics)"

1

Birman, M. S., and M. Z. Solomjak. "Commutation Relations of Quantum Mechanics." In Mathematics and Its Applications, 279–96. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-4586-9_12.

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Adelman, Steven A. "Commutation Rules and Uncertainty Relations." In Basic Molecular Quantum Mechanics, 91–97. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9780429155741-5.

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Faddeev, L., and O. Yakubovskiĭ. "Quantum mechanics of real systems. The Heisenberg commutation relations." In The Student Mathematical Library, 49–53. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/stml/047/10.

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Wigner, E. P. "Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?" In Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics, 95–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-09203-3_7.

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Arai, Asao. "Physical Correspondences in Quantum Field Theory." In Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations, 395–458. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2180-5_10.

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Sandhya, R. "Generalized Commutation Relations for Single Mode Oscillator." In Recent Developments in Quantum Optics, 105–8. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4615-2936-1_13.

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Ciaglia, F. M., G. Marmo, and L. Schiavone. "From Classical Trajectories to Quantum Commutation Relations." In Springer Proceedings in Physics, 163–85. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24748-5_9.

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Shankar, R. "The Heisenberg Uncertainty Relations." In Principles of Quantum Mechanics, 237–46. New York, NY: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-0576-8_9.

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Shankar, Ramamurti. "The Heisenberg Uncertainty Relations." In Principles of Quantum Mechanics, 245–54. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-7673-0_9.

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Bagarello, Fabio. "Deformed Canonical (anti-)commutation relations and non-self-adjoint hamiltonians." In Non-Selfadjoint Operators in Quantum Physics, 121–88. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118855300.ch3.

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Conference papers on the topic "Commutation relations (Quantum mechanics)"

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Ghirardi, GianCarlo. "The role of identity and entanglement in quantum mechanics." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337709.

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Arthurs, E., and M. S. Goodman. "Optical Implications of a new quantum correlation result." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.tua6.

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Recent advances, particularly in the area of quantum optics, have caused heightened interest in the fundamental limitations on the achievable accuracy that may be obtained in measuring quantum mechanical systems. We present a quantum correlation result and a noise commutation relation for correlated quantum systems. The measurement of quantum system observables requires the correlation of these micro-observables and the measuring apparatus (usually a macroscopic system). The noise commutation relation is applied to quantum measurements leading to a generalized Heisenberg uncertainty relation. The generalized Heisenberg uncertainty relation yields a lower bound on the inherent unavoidable extra noise in quantum measurements, which is due to the measuring process itself. To indicate the utility of the noise commutation relation, two different applications in optics are discussed. The first, an application of the generalized Heisenberg uncertainty relation, indicates how a model-independent noise limit for balanced homodyne detection can be obtained. Another application is discussed in which the noise commutation relation is applied to develop a model-independent lower bound for the inherent noise of a quantum optical linear amplifier.

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Salynsky, Sergey. "Quantum theory, canonical commutation relations." In The XIXth International Workshop on High Energy Physics and Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.104.0047.

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Smith, Brian J., N. Thomas-Peter, and I. A. Walmsley. "Two-Photon Interference and Commutation Relations." In Quantum Electronics and Laser Science Conference. Washington, D.C.: OSA, 2010. http://dx.doi.org/10.1364/qels.2010.qfa6.

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Otte, A. "Symmetry considerations in quantum computing." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337719.

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Solomon, Allan I. "Quon theories in quantum optics." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337723.

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Kirchner, Stefan. "Deformed quantum statistics of quons." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337724.

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Celeghini, Enrico. "Quantum statistics and dynamical algebras: Fermions." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337710.

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Dowker, H. F. "Spin and statistics in quantum gravity." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337730.

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Mishra, A. K. "Quantum field theory for orthofermions and orthobosons." In Spin-statistics connection and commutation relations. AIP, 2000. http://dx.doi.org/10.1063/1.1337726.

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Reports on the topic "Commutation relations (Quantum mechanics)"

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Soloviev, V. N., and Y. V. Romanenko. Economic analog of Heisenberg uncertainly principle and financial crisis. ESC "IASA" NTUU "Igor Sikorsky Kyiv Polytechnic Institute", May 2017. http://dx.doi.org/10.31812/0564/2463.

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The Heisenberg uncertainty principle is one of the cornerstones of quantum mechanics. The modern version of the uncertainty principle, deals not with the precision of a measurement and the disturbance it introduces, but with the intrinsic uncertainty any quantum state must possess, regardless of what measurement is performed. Recently, the study of uncertainty relations in general has been a topic of growing interest, specifically in the setting of quantum information and quantum cryptography, where it is fundamental to the security of certain protocols. The aim of this study is to analyze the concepts and fundamental physical constants in terms of achievements of modern theoretical physics, they search for adequate and useful analogues in the socio-economic phenomena and processes, and their possible use in early warning of adverse crisis in financial markets. The instability of global financial systems depending on ordinary and natural disturbances in modern markets and highly undesirable financial crises are the evidence of methodological crisis in modelling, predicting and interpretation of current socio-economic conditions.

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