Relevant bibliographies by topics / Dirac Notation

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Academic literature on the topic 'Dirac Notation'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Dirac Notation"

1

Xu, Yingte, Gilles Barthe, and Li Zhou. "Automating Equational Proofs in Dirac Notation." Proceedings of the ACM on Programming Languages 9, POPL (2025): 1227–59. https://doi.org/10.1145/3704878.

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Dirac notation is widely used in quantum physics and quantum programming languages to define, compute and reason about quantum states. This paper considers Dirac notation from the perspective of automated reasoning. We prove two main results: first, the first-order theory of Dirac notation is decidable, by a reduction to the theory of real closed fields and Tarski's theorem. Then, we prove that validity of equations can be decided efficiently, using term-rewriting techniques. We implement our equivalence checking algorithm in Mathematica, and showcase its efficiency across more than 100 exampl
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Stafford, Randall B., M. Louis Lauzon, Mohammad Sabati, Richard Frayne, and Robert I. Thompson. "A tutorial on the precessional behaviour of hydrogen nuclei in external magnetic fields." Canadian Journal of Physics 88, no. 7 (2010): 465–77. http://dx.doi.org/10.1139/p10-033.

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The purpose of this tutorial is to derive the precessional characteristics of the magnetic moments of hydrogen nuclei in the presence of a constant external magnetic field using the Dirac bra-ket formulation of quantum mechanics (QM). This behaviour has many applications, most notably in nuclear magnetic resonance (NMR) and magnetic resonance (MR) imaging. Many NMR and MR imaging textbooks claim that the QM expectation value of the magnetic moment of a proton in a magnetic field reduces to the classical picture of a precessing magnetic dipole. This paper validates this conclusion by reducing t
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Gao, Yipeng. "A Revisit to the Notation of Martensitic Crystallography." Crystals 8, no. 9 (2018): 349. http://dx.doi.org/10.3390/cryst8090349.

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As one of the most successful crystallographic theories for phase transformations, martensitic crystallography has been widely applied in understanding and predicting the microstructural features associated with structural phase transformations. In a narrow sense, it was initially developed based on the concepts of lattice correspondence and invariant plane strain condition, which is formulated in a continuum form through linear algebra. However, the scope of martensitic crystallography has since been extended; for example, group theory and graph theory have been introduced to capture the crys
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Dr., Kyongyob Min. "Dirac Bra-ket Notation for Interpreting Regional Distribution of Pulmonary Ventilation-Perfusion." International Journal of Case Studies 4, no. 1 (2015): 18–34. https://doi.org/10.5281/zenodo.3525611.

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Newly developing technologies of imaging have shown that the regional distribution of pulmonary ventilation and perfusion is formed from lobules of Miller in varying degrees of ventilation and perfusion. The theoretical study in this paper proposes using Dirac's bra-ket notation for describing the pulmonary ventilation-perfusion relations of the multiple inert-gas elimination technique (MIGET) based on the lobular lung model instead of the classical alveolar model. Bra-ket notation and the corresponding rules of calculation would provide a useful tool to solve the difficulties between pulm
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Dūdėnas, Vytautas, and Thomas Gajdosik. "Feynman rules for Weyl spinors with mixed Dirac and Majorana mass terms." Lithuanian Journal of Physics 56, no. 3 (2016): 149–63. http://dx.doi.org/10.3952/physics.v56i3.3364.

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We present a basic formalism for using the Weyl spinor notation in Feynman rules. We focus on Weyl spinors with mixed Dirac and Majorana mass terms. To clarify the definitions we derive the Feynman rules from the path integral and present two examples: loop corrections for a fermion propagator and a tree level analysis of a seesaw toy model.
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Rao, Allam Srinivasa. "An Intriguing Interpretation of 1D and 2D Non-Diffracting Modes in Cosine Profile." Photonics 10, no. 12 (2023): 1358. http://dx.doi.org/10.3390/photonics10121358.

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We provide a simple analysis based on ray optics and Dirac notation for 1D (one-dimensional) and 2D (two-dimensional) non-diffracting modes in the cosine profile, which are often called Cosine beams. We explore various kinds of structured modes formed by the superposition of two 1D Cosine beams. We then went on to understand the properties of the Bessel beams in terms of Cosine beams. For the first time, we report on the generation of three-dimensional tunable needle structures based on the interference of 1D Cosine beams. These size-tunable optical needles can have multiple advantages in mate
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Gunduz, Orhan, та Mustafa M. Aral. "A Dirac-δ Function Notation for Source/Sink Terms in Groundwater Flow". Journal of Hydrologic Engineering 10, № 5 (2005): 420–27. http://dx.doi.org/10.1061/(asce)1084-0699(2005)10:5(420).

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Cai, Ying, Cuihong Lv, Nan Huang, and Nan Jin. "Studying the Two New Convolutions of Fractional Fourier Transform by Using Dirac Notation." Journal of Contemporary Educational Research 6, no. 5 (2022): 38–47. http://dx.doi.org/10.26689/jcer.v6i5.3891.

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Based on quantum mechanical representation and operator theory, this paper restates the two new convolutions of fractional Fourier transform (FrFT) by making full use of the conversion relationship between two mutual conjugates: coordinate representation and momentum representation. This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics, a field that has been developing rapidly. These two new convolution methods have potential value in signal processing.
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LUNDBERG, WAYNE R. "SUFFICIENT EXTRA DIMENSIONS." International Journal of Modern Physics A 16, supp01c (2001): 998–1000. http://dx.doi.org/10.1142/s0217751x01008709.

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Matrix algebra notation in introduced which extends Dirac abstract vector notation to explicitly describe standard hadrons, leptons and a specific type of 1-brane. The 3×3×3 matrix notation is easily used with the path integral approach to model both strong and weak interactions. The specific 1-brane, called a tripartite string (a type of orientifold), has three extra spatial dimensions and three extra curvature dimensions which are necessary to describe standard particles. The extra spatial dimensions compactify to one area-like metric which, when scaled according to the Randall-Sundrum appro
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Khan, Farooq A., and John E. Hansen. "The Dirac (Bracket) Notation in the Undergraduate Physical Chemistry Curriculum: A Pictorial Introduction." Chemical Educator 5, no. 3 (2000): 113–19. http://dx.doi.org/10.1007/s00897000379a.

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Books on the topic "Dirac Notation"

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Horing, Norman J. Morgenstern. Dirac Notation and Transformation Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0001.

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Chapter 1 opens with a brief review of some basic features of quantum mechanics, including the Schrödinger equation, linear and angular momentum and the theory of the hydrogenic atom: It also includes complete orthonormal sets of eigenfunctions, the translation operator, current, spin, equation of continuity, gauge transformation, determinant & permanent multiparticle energy eigenfunctions for noninteracting particles and the Pauli exclusion principle. Attention is then focused on Dirac bra-ket notation and complete sets of commuting observables. In this connection, representations and tra
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An extension of Dirac notation. Lambert Academic Publishing, 2013.

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An extension of Dirac notation. The general science journal, 2009.

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Flarend, Alice, and Robert Hilborn. Quantum Computing: From Alice to Bob. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780192857972.001.0001.

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Quantum Computing: From Alice to Bob provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science (QIS) and quantum computing (QC). The book is designed for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics beyond secondary school algebra and trigonometry. While broadly accessible, the book provides a solid conceptual and formal understanding of quantum states and entanglement—the key ingredients in quantum computing. The authors give detailed treatments o
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Book chapters on the topic "Dirac Notation"

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Tumulka, Roderich. "Dirac Notation." In Compendium of Quantum Physics. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-70626-7_55.

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Berman, Paul R. "Dirac Notation." In Introductory Quantum Mechanics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68598-4_11.

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Hidary, Jack D. "Dirac Notation." In Quantum Computing: An Applied Approach. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83274-2_14.

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Xu, Yingte, Li Zhou, and Gilles Barthe. "D-Hammer: Efficient Equational Reasoning for Labelled Dirac Notation." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-98685-7_3.

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Abstract Labelled Dirac notation is a formalism commonly used by physicists to represent many-body quantum systems and by computer scientists to assert properties of quantum programs. It is supported by a rich equational theory for proving equality between expressions in the language. These proofs are typically carried on pen-and-paper, and can be exceedingly long and error-prone. We introduce D-Hammer, the first tool to support automated equational proof for labelled Dirac notation. The salient features of D-Hammer include: an expressive, higher-order, dependently-typed language for labelled
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Thyagarajan, K., and Ajoy Ghatak. "Vector Spaces and Linear Operators: Dirac Notation." In Lasers. Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-6442-7_8.

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Banks, Thomas. "Review of Linear Algebra and Dirac Notation." In Quantum Mechanics: An Introduction. CRC Press, 2018. http://dx.doi.org/10.1201/9780429438424-6.

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Jang, Seogjoo. "Dirac Notation and Principles of Quantum Mechanics." In Quantum Mechanics for Chemistry. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-30218-3_2.

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Do, Canh Minh, and Kazuhiro Ogata. "Equivalence Checking of Quantum Circuits Based on Dirac Notation in Maude." In Rewriting Logic and Its Applications. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-65941-6_5.

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9

Manousakis, Efstratios. "Dirac notation." In Practical Quantum Mechanics. Oxford University Press, 2015. http://dx.doi.org/10.1093/acprof:oso/9780198749349.003.0002.

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Duarte, F. J. "Dirac Notation Identities." In Quantum Optics for Engineers. CRC Press, 2017. http://dx.doi.org/10.1201/b16055-7.

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Conference papers on the topic "Dirac Notation"

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Singh, Chandralekha, and Emily Marshman. "Investigating Student Difficulties with Dirac Notation." In 2013 Physics Education Research Conference. American Association of Physics Teachers, 2014. http://dx.doi.org/10.1119/perc.2013.pr.074.

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Marshman, Emily, and Chandralekha Singh. "Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space." In 2020 Physics Education Research Conference. American Association of Physics Teachers, 2020. http://dx.doi.org/10.1119/perc.2020.pr.marshman.

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Marshman, Emily, and Chandralekha Singh. "Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations." In 2015 Physics Education Research Conference. American Association of Physics Teachers, 2015. http://dx.doi.org/10.1119/perc.2015.pr.048.

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