analytical mechanics for relativity and quantum mechanics oxford graduate texts

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Analytical Mechanics For Relativity And Quantum Mechanics

Author : Oliver Johns
ISBN : 019856726X
Genre : Mathematics
File Size : 29. 49 MB
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This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the graduate level. A distinguishing feature of the book is its integration of special relativity into the teaching of classical mechanics. Extended Lagrangian and Hamiltonian methods are introduced that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Lagrangians and Hamiltonians, canonical transformations, and the Hamilton-Jacobi equation are developed using this extended theory. This permits the Lorentz transformation of special relativity to become a canonical transformation. This is also a book for those who study analytical mechanics as a preliminary to a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text, and classical mechanics itself is presented in a way that will aid the reader in the study of quantum theory. A chapter is devoted to linear vector operators and dyadics, including a comparison to the bra-ket notation of quantum mechanics. Rotations are presented using an operator formalism similar to that used in quantum theory, and the definition of the Euler angles follows the quantum mechanical convention. The extended Hamiltonian theory with time as a coordinate is compared to Dirac's formalism of primary phase space constraints. The chapter on relativistic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics. The book provides a necessary bridge to carry graduate students from their previous undergraduate classical mechanics courses to the future study of advanced relativity and quantum theory. Several of the current fundamental problems in theoretical physics---the development of quantum information technology, and the problem of quantizing the gravitational field, to name two---require a rethinking of the quantum-classical connection. This text is intended to encourage the retention or restoration of introductory graduate analytical mechanics courses. It is written for the intellectually curious graduate student, and the teacher who values mathematical precision in addition to accessibility.

The Physics Of Quantum Mechanics

Author : James Binney
ISBN : 9780199688579
Genre : Science
File Size : 67. 75 MB
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"First published by Cappella Archive in 2008."

Analytic Hyperbolic Geometry And Albert Einstein S Special Theory Of Relativity

Author : Abraham A. Ungar
ISBN : 9789812772299
Genre : Science
File Size : 51. 77 MB
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This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors. Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative. The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami–Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky. Similarly, Mצbius addition gives rise to gyrovector spaces that form the algebraic setting for the Poincarי ball model of hyperbolic geometry. In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. The novel relativistic resultant mass of the system, concentrated at the relativistic center of mass, dictates the validity of the dark matter and the dark energy that were introduced by cosmologists as ad hoc postulates to explain cosmological observations about missing gravitational force and late-time cosmic accelerated expansion. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying analytic hyperbolic geometry.

Solved Problems In Classical Mechanics

Author : O.L. de Lange
ISBN : 9780199582525
Genre : Mathematics
File Size : 26. 80 MB
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simulated motion on a computer screen, and to study the effects of changing parameters. --

Antimaterie

Author : Frank Close
ISBN : 382742531X
Genre : Science
File Size : 54. 90 MB
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Genesis Im Anfang w ar Leere: „Finsternis lag über der Ur ut“. Dann kam es zu einem gewaltigen Energieausbruch: „Es werde Licht. Und es wurde Licht.“ Woher diese Energie kam, weiß ich nicht. Bekannt ist jedoc h, was anschließend geschah: Die Energie kondensierte zu Materie und ihrem geheimn- vollen Spiegelbild – der Antimaterie – in vollkommen gl- chen Mengen. Gewöhnliche Materie ist uns vertraut; aus ihr bestehen Luft und Erde und die Lebewesen. Doch ihr getreues, in allen Erscheinungen identisches Spiegelbild, das erst im Inneren der Atome seine „verkehrte“ Natur offenbart, ist uns mehr als fremd. Es ist die Antimaterie, die Antithese zur Materie. Antimaterie gibt es heute nicht in größeren Mengen, zumindest nicht auf der Erde. Der Grund für ihr V- schwinden gehört zu den unerklärten Geheimnissen des Universums. Wir wissen aber, dass Antimaterie existiert, denn sie konnte in physikalischen Experimenten in win- gen Mengen hergestellt werden. Antimaterie zerstört jede gewöhnliche Materie, mit der sie in Berührung kommt, in einem grellen Blitz. Die seit XII Vorwort Milliarden von Jahren gebündelte Energie der Materie wird in einem solchen Augenblick explosionsartig frei- setzt. Antimaterie könnte die ideale Energiequelle werden, die Technologie des 21. Jahrhunderts. Doch ihre Fähigkeit zur absoluten Zerstörung könnte sie auch zu einer ulti- tiven Massenvernichtungswaffe machen.

Author : Lev Davidovich Landau
ISBN : 0750635398
Genre : Science
File Size : 23. 96 MB
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This edition has been completely revised to include some 20% of new material. Important recent developments such as the theory of Regge poles are now included. Many problems with solutions have been added to those already contained in the book.

Mathematical Reviews

Author :
ISBN : UOM:39015076649873
Genre : Mathematics
File Size : 86. 90 MB
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Statistical Benchmarks For Quantum Transport In Complex Systems

Author : Mattia Walschaers
ISBN : 9783319931517
Genre : Science
File Size : 74. 13 MB
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This book introduces a variety of statistical tools for characterising and designing the dynamical features of complex quantum systems. These tools are applied in the contexts of energy transfer in photosynthesis, and boson sampling. In dynamical quantum systems, complexity typically manifests itself via the interference of a rapidly growing number of paths that connect the initial and final states. The book presents the language of graphs and networks, providing a useful framework to discuss such scenarios and explore the rich phenomenology of transport phenomena. As the complexity increases, deterministic approaches rapidly become intractable, which leaves statistics as a viable alternative.

Mechanik

Author : Florian Scheck
ISBN : 9783662085936
Genre : Science
File Size : 59. 44 MB
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Die vierte Auflage der Mechanik wurde in einigen Abschnitten ergänzt (z.B. zur Hamiltonschen Prinzipialfunktion und zum Aufstehkreisel) und auf Fehler durchgesehen, zudem wurden die Aufgaben überarbeitet, wobei nun alle vollständigen Lösungen mit aufgenommen wurden. Das wird all jenen zugute kommen, die diese umfassende Einführung in die Mechanik vorlesungsbegleitend oder zum Selbststudium verwenden wollen. Am Grundaufbau des Buches wurde nichts geändert: von elementarer Newtonscher Mechanik bis zur Diskussion von deterministischem Chaos und kontinuierlichen Systemen. Ein mathematischer Anhang und ein Wegweiser durch die Literatur runden das Buch ab.

Operator Methods In Quantum Mechanics

Author : O. L. De Lange
ISBN : UOM:39015024990148
Genre : History
File Size : 56. 75 MB
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Quantum mechanical problems capable of exact solution are traditionally solved in a few instances only (such as the harmonic oscillator and angular momentum) by operator methods, but mainly by means of Schrodinger's wave mechanics. The present volume shows that a large range of one- and three- dimensional problems, including certain relativistic ones, are solvable by algebraic, representation-independent methods using commutation relations, shift operators, the viral, hyperviral, and Hellman-Feynman theorems. Applications of these operator methods to the calculation of eigenvalues, matrix elements, and wavefunctions are discussed in detail. This volume provides an outstanding introduction to the use of operator methods in quantum mechanics, and also serves as a reference work on this topic. As such it is an excellent complement to senior and graduate courses in quantum mechanics. Although primarily a book on applications of operator methods, the presentation is made self-contained by the inclusion of an introductory chapter on the formalism of quantum mechanics. Additional background material supplements the volume at various points in the text. Although there has been much research on operator methods to solve quantum mechanical problems, until now many of these results have remained scattered throughout the literature. Nonspecialists, as well as graduate and upper division students in physics will find this accessible volume to be essential reading in theoretical physics.

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