Relevant bibliographies by topics / Heisenberg uncertainty principle

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Academic literature on the topic 'Heisenberg uncertainty principle'

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Published: 4 June 2021
Last updated: 8 June 2024

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Journal articles on the topic "Heisenberg uncertainty principle"

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Barukčić, Ilija. "Anti Heisenberg – Refutation of Heisenberg’s Uncertainty Principle." International Journal of Applied Physics and Mathematics 4, no. 4 (2014): 244–50. http://dx.doi.org/10.7763/ijapm.2014.v4.292.

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Peijnenburg, Jeanne, and David Atkinson. "Hoe zeker is Heisenbergs onzekerheidsprincipe?" Algemeen Nederlands Tijdschrift voor Wijsbegeerte 113, no. 1 (February 1, 2021): 137–56. http://dx.doi.org/10.5117/antw2021.1.006.peij.

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Abstract How certain is Heisenberg’s uncertainty principle? Heisenberg’s uncertainty principle is at the heart of the orthodox or Copenhagen interpretation of quantum mechanics. We first sketch the history that led up to the formulation of the principle. Then we recall that there are in fact two uncertainty principles, both dating from 1927, one by Werner Heisenberg and one by Earle Kennard. Finally, we explain that recent work in physics gives reason to believe that the principle of Heisenberg is invalid, while that of Kennard still stands.
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Jesi Pebralia. "PRINSIP KETIDAKPASTIAN HEISENBERG DALAM TINJAUAN KEMAJUAN PENGUKURAN KUANTUM DI ABAD 21." JOURNAL ONLINE OF PHYSICS 5, no. 2 (July 25, 2020): 43–47. http://dx.doi.org/10.22437/jop.v5i2.9049.

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The Heisenberg uncertainty principle is the basic foundation of quantum physics that characterizes quantum physics with classical physics. The Heisenberg uncertainty principle provides boundaries where there are no absolute measurement results in any quantum measurement. Along with the development of increasingly sophisticated measurement instruments in the 21st century, presents the opportunity for the emergence of modifications from the Heisenberg uncertainty principle from the general form of existing formulations. This study aims to provide an overview of the opportunities for Heisenberg uncertainty formulation and provide a description of the stages of the Heisenberg uncertainty formulation's uncertainty formulations that have been reviewed by previous researchers. The research method used is the method of literature study that aims to find out the background and theories of the development of Heisenberg's uncertainty principle and to explain the formulation directly which aims to determine the technical sequence of modifications to the existing formulation. Through this research, the authors managed to get an opportunity for the emergence of new modifications to the Heisenberg uncertainty principle formulation.
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Cao, Zhaozhong. "Uncertainty principle and complementary variables." Highlights in Science, Engineering and Technology 61 (July 30, 2023): 18–23. http://dx.doi.org/10.54097/hset.v61i.10260.

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The two most important areas in modern physics are quantum mechanics and the theory of relativity. Unlike classical physics, where Newton's mechanics dominates, these two areas change human beings' fundamental view of the universe. One of the theories that build up the base of quantum mechanics is Heisenberg's Uncertainty Principle. Starting from a thought experiment, Heisenberg's microscope in the setting of classical physics, Werner Heisenberg built a bridge between classical and quantum physics by presenting a counterintuitive outcome in the thought experiment. Since then, the observer of a physics phenomenon is no longer a bystander. The behavior of observation became a part of the physical experiment. To come up with a mathematical expression that can describe such a new discovery, Heisenberg came up with matrix mechanics and the concept of complementary variables. There is a trade-off between a pair of complementary variables. When one of them is measured precisely, meaning the information of that variable is known on a large scale, the other variable can not be measured precisely, meaning there is no way to know enough information about the other variable. The principle indicates a fundamental limit on what human beings can know about the unknown variables. The discoveries of other complementary variables help physicists know the new image of the physics world under new rules.
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Putra, Fima Ardianto. "On the Semiclassical Approach of the Heisenberg Uncertainty Relation in the Strong Gravitational Field of Static Blackhole." Jurnal Fisika Indonesia 22, no. 2 (April 16, 2020): 15. http://dx.doi.org/10.22146/jfi.v22i2.34274.

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Heisenberg Uncertainty and Equivalence Principle are the fundamental aspect respectively in Quantum Mechanic and General Relativity. Combination of these principles can be stated in the expression of Heisenberg uncertainty relation near the strong gravitational field i.e. pr and Et . While for the weak gravitational field, both relations revert to pr and Et. It means that globally, uncertanty principle does not invariant. This work also shows local stationary observation between two nearby points along the radial direction of blackhole. The result shows that the lower point has larger uncertainty limit than that of the upper point, i.e. . Hence locally, uncertainty principle does not invariant also. Through Equivalence Principle, we can see that gravitation can affect Heisenberg Uncertainty relation. This gives the impact to our’s viewpoint about quantum phenomena in the presence of gravitation. Key words: Heisenberg Uncertainty Principle , Equivalence Principle, and gravitational field
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Fei, Minggang, Yubin Pan, and Yuan Xu. "Some shaper uncertainty principles for multivector-valued functions." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (November 2016): 1650043. http://dx.doi.org/10.1142/s0219691316500430.

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The Heisenberg uncertainty principle and the uncertainty principle for self-adjoint operators have been known and applied for decades. In this paper, in the framework of Clifford algebra, we establish a stronger Heisenberg–Pauli–Wely type uncertainty principle for the Fourier transform of multivector-valued functions, which generalizes the recent results about uncertainty principles of Clifford–Fourier transform. At the end, we consider another stronger uncertainty principle for the Dunkl transform of multivector-valued functions.
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Barukčić, Ilija. "Anti Heisenberg—The End of Heisenberg’s Uncertainty Principle." Journal of Applied Mathematics and Physics 04, no. 05 (2016): 881–87. http://dx.doi.org/10.4236/jamp.2016.45096.

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Wulandari, Dewi. "Mathematics Behind the Heisenberg Uncertainty Principle." Jurnal Penelitian Pendidikan IPA 9, no. 4 (April 30, 2023): 2223–28. http://dx.doi.org/10.29303/jppipa.v9i4.3545.

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Most physics books do not reveal clearly how the Heisenberg uncertainty principle was derived. This uncertainty comes from the consequence of the wave-particle duality of matter giving statement that position and momentum cannot be measured in the same time. This article tries to reveal mathematics background behind the expression the Heisenberg uncertainty using supported mathematics background such as Fourier transform, Fourier transform integral, the probability of Gaussian distribution and it ends up with the expression of wave function which describe the localized particle giving relation Heisenberg uncertainty principle.
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Beckwith, A. W., and S. S. Moskaliuk. "Generalized Heisenberg Uncertainty Principle in Quantum Geometrodynamics and General Relativity." Ukrainian Journal of Physics 62, no. 8 (September 2017): 727–40. http://dx.doi.org/10.15407/ujpe62.08.0727.

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Hleili, Khaled. "A variety of uncertainty principles for the Hankel-Stockwell transform." Open Journal of Mathematical Analysis 5, no. 1 (January 29, 2021): 22–34. http://dx.doi.org/10.30538/psrp-oma2021.0079.

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In this work, we establish \(L^p\) local uncertainty principle for the Hankel-Stockwell transform and we deduce \(L^p\) version of Heisenberg-Pauli-Weyl uncertainty principle. Next, By combining these principles and the techniques of Donoho-Stark we present uncertainty principles of concentration type in the \(L^p\) theory, when \(1< p\leqslant2\). Finally, Pitt's inequality and Beckner's uncertainty principle are proved for this transform.
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Dissertations / Theses on the topic "Heisenberg uncertainty principle"

1

Akten, Burcu Elif. "Generalized uncertainty relations /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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Chan, Chi Hung. "3-dimensional Heisenberg antiferromagnet in cubic lattice under time periodic magnetic field /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202009%20CHANC.

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Rekuc, Steven Joseph. "Eliminating Design Alternatives under Interval-Based Uncertainty." Thesis, Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7218.

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Typically, design is approached as a sequence of decisions in which designers select what they believe to be the best alternative in each decision. While this approach can be used to arrive at a final solution quickly, it is unlikely to result in the most-preferred solution. The reason for this is that all the decisions in the design process are coupled. To determine the most preferred alternative in the current decision, the designer would need to know the outcomes of all future decisions, information that is currently unavailable or indeterminate. Since the designer cannot select a single alternative because of this indeterminate (interval-based) uncertainty, a set-based design approach is introduced. The approach is motivated by the engineering practices at Toyota and is based on the structure of the Branch and Bound Algorithm. Instead of selecting a single design alternative that is perceived as being the most preferred at the time of the decision, the proposed set-based design approach eliminates dominated design alternatives: rather than selecting the best, eliminate the worst. Starting from a large initial design space, the approach sequentially reduces the set of non-dominated design alternatives until no further reduction is possible ??e remaining set cannot be rationally differentiated based on the available information. A single alternative is then selected from the remaining set of non-dominated designs. In this thesis, the focus is on the elimination step of the set-based design method: A criterion for rational elimination under interval-based uncertainty is derived. To be efficient, the criterion takes into account shared uncertainty ??certainty shared between design alternatives. In taking this uncertainty into account, one is able to eliminate significantly more design alternatives, improving the efficiency of the set-based design approach. Additionally, the criterion uses a detailed reference design to allow more elimination of inferior design sets without evaluating each alternative in that set. The effectiveness of this elimination is demonstrated in two examples: a beam design and a gearbox design.
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Shiri-Garakani, Mohsen. "Finite Quantum Theory of the Harmonic Oscillator." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5078.

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We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N=l(l+1) states where l is very large for physically interesting case. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N there are three broad classes of FLHO: soft, medium, and hard corresponding respectively to cases where ratio of the of potential energy to kinetic energy in the Hamiltonian is very small, almost equal to one, or very large The field oscillators responsible for infra-red and ultraviolet divergences are soft and hard respectively. Medium oscillators approximate the QLHO. Their low-lying states have nearly the same zero-point energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z-axis. The soft and hard FLHO's have infinitesimal 0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators polaroizd along x-axis or y-axis respectively. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
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Durham, Ian T. "Sir Arthur Eddington and the foundations of modern physics." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/12933.

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In this dissertation I analyze Sir Arthur Eddington's statistical theory as developed in the first six chapters of his posthumously published Fundamental Theory. In particular I look at the mathematical structure, philosophical implications, and relevancy to modern physics. This analysis is the only one of Fundamental Theory that compares it to modern quantum field theory and is the most comprehensive look at his statistical theory in four decades. Several major insights have been made in this analysis including the fact that he was able to derive Pauli's Exclusion Principle in part from Heisenberg's Uncertainty Principle. In addition the most profound general conclusion of this research is that Fundamental Theory is, in fact, an early quantum field theory, something that has never before been suggested. Contrary to the majority of historical reports and some comments by his contemporaries, this analysis shows that Eddington's later work is neither mystical nor was it that far from mainstream when it was published. My research reveals numerous profoundly deep ideas that were ahead of their time when Fundamental Theory was developed, but that have significant applicability at present. As such this analysis presents several important questions to be considered by modern philosophers of science, physicists, mathematicians, and historians. In addition it sheds new light on Eddington as a scientist and mathematician, in part indicating that his marginalization has been largely unwarranted.
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Kelley, Logan. "The Quantum Dialectic." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/pitzer_theses/4.

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A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part I includes in-depth discussions of mathematical principles. Part II will discuss the Copenhagen interpretation as put forth by its founders. The Copenhagen interpretation will be expressed as a paradox: The classical physical language cannot describe quantum phenomenon completely and with certainty, yet this language is the only possible method of articulating the physical world. The paradox of Copenhagen will segway into Kant's critique of metaphysics. Kant's understanding of causality, things-in-themselves, and a priori synthetic metaphysics. The thesis will end with a conclusion of the quantum paradox by juxtaposing anti-materialist Martin Heidegger with quantum founder Werner Heisenberg. Our conclusion will be primarily a discussion of how we understand the world, and specifically how our understanding of the world creates potential for truth.
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Scipioni, Angel. "Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles." Electronic Thesis or Diss., Nancy 1, 2010. http://www.theses.fr/2010NAN10125.

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La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonore
The necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that characterizes magnetized plasmas. Finally, we will point out the reasons that show the lack of link between high values of the Hurst coefficient and possible long correlations. The third chapter is dedicated to the second application domain which is relative to the backscattered echo analysis of an immersed target insonified by an ultrasonic plane wave. We will explain how a morphological approach associated to a scale analysis can extract the diameter information
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Scipioni, Angel. "Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles." Thesis, Nancy 1, 2010. http://www.theses.fr/2010NAN10125.

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La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonore
The necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that characterizes magnetized plasmas. Finally, we will point out the reasons that show the lack of link between high values of the Hurst coefficient and possible long correlations. The third chapter is dedicated to the second application domain which is relative to the backscattered echo analysis of an immersed target insonified by an ultrasonic plane wave. We will explain how a morphological approach associated to a scale analysis can extract the diameter information
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9

Guerra, Rita Catarina Correia. "Generalizations of the Fourier transform and their applications." Doctoral thesis, 2019. http://hdl.handle.net/10773/29813.

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In this thesis, we consider a new generalization of the Fourier transform, depending on four complex parameters and all the powers of the Fourier transform. This new transform is studied in some Lebesgue spaces. In fact, taking into account the values of the parameters of the operator, we can have very different kernels and so, the corresponding operator is studied in different Lebesgue spaces, accordingly with its kernel. We begin with the characterization of each operator by its characteristic polynomial. This characterization serves as a basis for the study of the forthcoming properties. Following this, we present, for each case, the spectrum of the corresponding operator, necessary and sufficient conditions for which the operator is invertible, Parseval-type identities and conditions for which the operator is unitary and an involution of order n. After this, we contruct new convolutions associated with those operators and obtain the corresponding factorization identities and some norm inequalities. By using these new operators and convolutions, we construct new integral equations and study their solvability. In this sense, we have equations generated by the studied operators and also a class of equations of convolution-type depending on multi-dimensional Hermite functions. Furthermore, we study the solvability of classical integral equations, using the new operators and convolutions, namely a class of Wiener-Hopf plus Hankel equations, whose solution is written in terms of a Fourier-type series. For one case of this generalization of the Fourier transform, that only depends on the cosine and sine Fourier transforms, we obtain PaleyWiener and Wiener’s Tauberian results, using the associated convolution and a new translation induced by that convolution. Heisenberg uncertainty principles for the one-dimensional case and for the multi-dimensional case are obtained for a particular case of the introduced operator. At the end, as an application outside of mathematics, we obtain a new result in signal processing, more properly, in a filtering processing, by applying one of our new convolutions.
Nesta tese, consideramos uma nova generalização da transformação de Fourier, dependente de quatro parâmetros complexos e de todas as potências da transformação de Fourier. Esta nova transformação é estudada em alguns espaços de Lebesgue. De facto, tendo em conta os valores dos parâmetros, podemos ter núcleos muito diferentes e assim, o correspondente operador é estudado em diferentes espaços de Lebesgue, de acordo com o seu núcleo. Começamos com a caracterização de cada operador pelo seu polinómio característico. Esta caracterização serve de base para o estudo das propriedades seguintes. Seguindo isto, apresentamos, para cada caso, o espetro do correspondente operador, condições necessárias e suficientes para as quais o operador é invertível, identidades do tipo de Parseval e condições para as quais o operador é unitário e uma involução de ordem n. Depois disto, construímos novas convoluções associadas àqueles operadores e obtemos as correspondentes identidades de factorização e algumas desigualdades da norma. Usando estes novos operadores e convoluções, construímos novas equações integrais e estudamos a sua solvabilidade. Neste sentido, temos equações geradas pelos operadores estudados e também uma classe de equações do tipo de convolução dependendo de funções de Hermite multidimensionais. Além disso, estudamos a solvabilidade de equações integrais clássicas, usando os novos operadores e convoluções, nomeadamente uma classe de equações de Wiener-Hopf mais Hankel, cuja solução é escrita em termos de uma série do tipo de Fourier. Para um caso desta generalização da transformação de Fourier, que depende apenas das transformações de Fourier do cosseno e do seno, obtemos resultados de Paley-Wiener e resultados Tauberianos de Wiener, usando a convolução associada e uma nova translação induzida por essa convolução. Princípios de incerteza de Heisenberg para os casos unidimensional e multidimensional são obtidos para um caso particular do operador introduzido. No final, como uma aplicação fora da matemática, obtemos um novo resultado em processamento de sinal, mais propriamente, num processo de filtragem, por aplicação de uma das nossas novas convoluções.
Programa Doutoral em Matemática Aplicada
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10

Ganguly, Pritam. "Quasi-analytic Functions, Spherical Means, and Uncertainty Principles on Heisenberg Groups and Symmetric Spaces." Thesis, 2022. https://etd.iisc.ac.in/handle/2005/5697.

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This thesis has two parts. The first part revolves around certain theorems related to an uncertainty principle and quasi-analyticity. In contrast, the second part reflects a different mathematical theme, focusing on the classical problem of $L^p$ boundedness of spherical maximal function on the Heisenberg group. The highlights of the first part are as follows: An uncertainty principle due to Ingham (proved initially on $\R$) investigates the best possible decay admissible for the Fourier transform of a function that vanishes on a nonempty open set. One way to establish such a result is to use a theorem of Chernoff (proved originally on $\mathbb{R}^n$), which provides a sufficient condition for a smooth function to be quasi-analytic in terms of a Carleman condition involving powers of the Laplacian. In this part of this thesis, we aim to prove various analogues of theorems of Ingham and Chernoff in different contexts such as the Heisenberg group, Hermite and special Hermite expansions, rank one Riemannian symmetric spaces and Euclidean space with Dunkl setting. More precisely, we prove various analogues of Chernoff's theorem for the full Laplacian on the Heisenberg group, Hermite and special Hermite operators, Laplace-Beltrami operators on rank one symmetric spaces of both compact and non-compact type, and Dunkl Laplacian. The main idea is to reduce the situation to the radial case by employing appropriate spherical means or spherical harmonics and then to apply Chernoff type theorems to the radial parts of the operators indicated above. Using those Chernoff type theorems, we then show several analogues of Ingham's theorem for the spectral projections associated with those aforementioned operators. Furthermore, we provide examples of compactly supported functions with Ingham type decay in their spectral projections, demonstrating the sharpness of Ingham's theorem in all of the relevant contexts mentioned above. In this second part of this thesis, we investigate the $L^p$ boundedness of the lacunary maximal function $ M_{\Ha}^{lac} $ associated to the spherical means $ A_r f$ taken over Koranyi spheres on the Heisenberg group. Closely following an approach used by M. Lacey in the Euclidean case, we obtain sparse bounds for these maximal functions leading to new unweighted and weighted estimates. The key ingredients in the proof are the $L^p$ improving property of the operator $A_rf$ and a continuity property of the difference $A_rf-\tau_y A_rf$, where $\tau_yf(x)=f(xy^{-1})$ is the right translation operator.
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Books on the topic "Heisenberg uncertainty principle"

1

Füting, Manfred. Werner Heisenberg und die Unschärferelation: Ihre Bedeutung für die Determinismusauffassung und für die These von der Erkennbarkeit der Welt. Weimar: Redaktion der Wissenschaftlichen Zeitschrift und Publikationen Hochschule für Architektur und Bauwesen Weimar, 1987.

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Cendon, Fernando Blanco. En torno al principio de indeterminación de Werner Karl Heisenberg. Madrid: Instituto Pontificio de Filosofía, 1986.

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Gonzalo, Julio A. Cosmological implications of Heisenberg's principle. Singapore: World Scientific, 2015.

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de, Broglie Louis. Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics: With critical notes of the author. Dordrecht: Kluwer Academic Publishers, 1990.

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Sándor, Koch, and Juhász-Nagy Pál, eds. A Tökéletlenség és korlátosság dicsérete. Budapest: Gondolat, 1989.

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To phantasma tēs operas: Hē epistēmē ston politismo mas. Hērakleio, Krētēs: Panepistēmiakes Ekdoseis Krētēs, 2014.

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1974-, Pods Sonja, ed. The geometry of Heisenberg groups in signal theory, optics, quantization, and field quantization. Providence, R.I: American Mathematical Society, 2008.

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NATO Advanced Study Institute on Sixty-two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics (1989 Erice, Italy). Sixty-two years of uncertainty: Historical, philosophical, and physical inquiries into the foundations of quantum mechanics. New York: Plenum Press, 1990.

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National Science Foundation (U.S.), ed. Toeplitz approach to problems of the uncertainty principle. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2015.

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Theology and scientific knowledge: Changing models of God's presence in the world. Notre Dame: University of Notre Dame Press, 1996.

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Book chapters on the topic "Heisenberg uncertainty principle"

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Rajasekar, S., and R. Velusamy. "Heisenberg Uncertainty Principle." In Quantum Mechanics I, 205–22. 2nd ed. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003172178-8.

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Gooch, Jan W. "Heisenberg Uncertainty Principle." In Encyclopedic Dictionary of Polymers, 362. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_5881.

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Holbrow, Charles H., James N. Lloyd, Joseph C. Amato, Enrique Galvez, and M. Elizabeth Parks. "The Heisenberg Uncertainty Principle." In Modern Introductory Physics, 553–67. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-79080-0_18.

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Holbrow, C. H., J. N. Lloyd, and J. C. Amato. "The Heisenberg Uncertainty Principle." In Modern Introductory Physics, 407–23. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4757-3078-4_15.

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Thangavelu, Sundaram. "Heisenberg Groups." In An Introduction to the Uncertainty Principle, 45–104. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8164-7_2.

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Pérez-Marco, Ricardo. "Blockchain Time and Heisenberg Uncertainty Principle." In Advances in Intelligent Systems and Computing, 849–54. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01174-1_66.

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Capozziello, Salvatore, and Wladimir-Georges Boskoff. "The Heisenberg Uncertainty Principle and the Mathematics Behind." In UNITEXT for Physics, 145–71. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86098-1_8.

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Williams, Floyd. "Heisenberg’s Uncertainty Principle." In Topics in Quantum Mechanics, 157–70. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0009-3_7.

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Stannard, Russell. "Heisenberg’s Uncertainty Principle." In Encyclopedia of Sciences and Religions, 979. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-1-4020-8265-8_200566.

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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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Conference papers on the topic "Heisenberg uncertainty principle"

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D'Angelo, Milena, Morton H. Rubin, and Yanhua Shih. "EPR inequality and Heisenberg uncertainty principle." In International Quantum Electronics Conference. Washington, D.C.: OSA, 2004. http://dx.doi.org/10.1364/iqec.2004.ituj6.

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Singh, Gurkirat, Aman Singh, and N. M. Sreenarayanan. "Quantum Cryptography with Photon Polarization and Heisenberg Uncertainty Principle." In 2022 2nd International Conference on Advance Computing and Innovative Technologies in Engineering (ICACITE). IEEE, 2022. http://dx.doi.org/10.1109/icacite53722.2022.9823504.

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Huo, Mandy, Aristotelis Asimakopoulos, and John C. Doyle. "Measurement back action and a classical uncertainty principle: Heisenberg meets Kalman." In 2019 American Control Conference (ACC). IEEE, 2019. http://dx.doi.org/10.23919/acc.2019.8814965.

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Frieden, B. Roy. "Fisher information and error complimentarity." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.fl3.

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The Cramer-Rao (CR) inequality e2I ≥ 1 represents complimentarity between (i) the size of mean-squares error e2 in estimation of a parameter θ from an observation y where y = θ + x, and (ii) the Fisher information I due to pdf p(x). In application to quantum mechanics, θ is the classical position of a particle, and I becomes the mean-squares momentum spread for the particle. Thus, the CR inequality becomes the Heisenberg uncertainty principle. The latter is, then, but one example of a general principle of error complimentarity. As applied to optical diffraction, θ is now the unknown centroid of a diffraction pattern. Here the CR inequality becomes e2z2 ≥ (λf/4π)2, where z2 is the mean-squares photon position in the lens pupil, λ is the light wavelength, and f is the focal length. Interestingly, here the uncertainty product can be made arbitrarily small. Another use is in the case of a nonideal gas kept at a constant temperature T. The gas is inside a container of unknown drift velocity θ. If p(x) defines the probability law on velocity x for particles of the gas, the CR inequality attains a minimum for the uncertainty product e2I when p(x) is Gaussian, i.e., when p(x) is a Boltzmann law. This describes the ideal gas scenario and gives it a new significance.
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Castro, L. P., R. C. Guerra, and N. M. Tuan. "Heisenberg uncertainty principles for an oscillatory integral operator." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972629.

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SCHIPPER, HYMAN M., and RABBI RAPHAEL AFILALO. "Did the Kabbalah Anticipate Heisenberg’s Uncertainty Principle?" In Unified Field Mechanics II: Preliminary Formulations and Empirical Tests, 10th International Symposium Honouring Mathematical Physicist Jean-Pierre Vigier. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813232044_0032.

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Young, Jeffrey L., and Christopher D. Wilson. "An application of Heisenberg's Uncertainty principle to line source radiation." In 2015 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2015. http://dx.doi.org/10.1109/aps.2015.7304918.

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Karlsson, Anders, Lars Gillner, Edgard Goobar, and Gunnar Björk. "Networks with quantum amplifiers." In The European Conference on Lasers and Electro-Optics. Washington, D.C.: Optica Publishing Group, 1994. http://dx.doi.org/10.1364/cleo_europe.1994.cthd1.

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As the best fibre optical systems are approaching fundamental quantum limits, the role of Heisenberg's uncertainty principle in communications has shifted from being of academic interest to becoming an (un)practical restriction.
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Ribak, Erez N., and Gal Gumpel. "Beyond the Quantum Optical Diffraction Limit." In Imaging Systems and Applications. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/isa.2022.itu3e.1.

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To circumvent Heisenberg’s uncertainty principle, we multiplied the number of white light photons using a dye. With larger wave-packets, the resolution is improved, as if with a larger aperture, but longer integration times are necessary.
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Prasad, Narasimha S., and Chandrasekhar Roychoudhuri. "Microscope and spectroscope results are not limited by Heisenberg's Uncertainty Principle!" In SPIE Optical Engineering + Applications, edited by Chandrasekhar Roychoudhuri, Andrei Yu Khrennikov, and Al F. Kracklauer. SPIE, 2011. http://dx.doi.org/10.1117/12.895207.

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Reports on the topic "Heisenberg uncertainty principle"

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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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Соловйов, Володимир Миколайович, and V. Saptsin. Heisenberg uncertainty principle and economic analogues of basic physical quantities. Transport and Telecommunication Institute, 2011. http://dx.doi.org/10.31812/0564/1188.

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From positions, attained by modern theoretical physics in understanding of the universe bases, the methodological and philosophical analysis of fundamental physical concepts and their formal and informal connections with the real economic measuring is carried out. Procedures for heterogeneous economic time determination, normalized economic coordinates and economic mass are offered, based on the analysis of time series, the concept of economic Plank's constant has been proposed. The theory has been approved on the real economic dynamic's time series, including stock indices, Forex and spot prices, the achieved results are open for discussion.
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Bielinskyi, Andriy, Serhiy Semerikov, Oleksandr Serdiuk, Victoria Solovieva, Vladimir Soloviev, and Lukáš Pichl. Econophysics of sustainability indices. [б. в.], October 2020. http://dx.doi.org/10.31812/123456789/4118.

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In this paper, the possibility of using some econophysical methods for quantitative assessment of complexity measures: entropy (Shannon, Approximate and Permutation entropies), fractal (Multifractal detrended fluctuation analysis – MF-DFA), and quantum (Heisenberg uncertainty principle) is investigated. Comparing the capability of both entropies, it is obtained that both measures are presented to be computationally efficient, robust, and useful. Each of them detects patterns that are general for crisis states. The similar results are for other measures. MF-DFA approach gives evidence that Dow Jones Sustainability Index is multifractal, and the degree of it changes significantly at different periods. Moreover, we demonstrate that the quantum apparatus of econophysics has reliable models for the identification of instability periods. We conclude that these measures make it possible to establish that the socially responsive exhibits characteristic patterns of complexity, and the proposed measures of complexity allow us to build indicators-precursors of critical and crisis phenomena.
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Chen, Yu. Inverse Scattering via Heisenberg's Uncertainty Principle. Fort Belvoir, VA: Defense Technical Information Center, February 1996. http://dx.doi.org/10.21236/ada305113.

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Soloviev, V., V. Solovieva, and V. Saptsin. Heisenberg uncertainity principle and economic analogues of basic physical quantities. Брама-Україна, 2014. http://dx.doi.org/10.31812/0564/1306.

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From positions, attained by modern theoretical physics in understanding of the universe bases, the methodological and philosophical analysis of fundamental physical concepts and their formal and informal connections with the real economic measurings is carried out. Procedures for heterogeneous economic time determination, normalized economic coordinates and economic mass are offered, based on the analysis of time series, the concept of economic Plank's constant has been proposed. The theory has been approved on the real economic dynamic's time series, including stock indices, Forex and spot prices, the achieved results are open for discussion.
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