spectral theory and quantum mechanics unitext

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Spectral Theory And Quantum Mechanics

Author : Valter Moretti
ISBN : 9788847028357
Genre : Mathematics
File Size : 69. 59 MB
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This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out to Master's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.

Advances In Algebraic Quantum Field Theory

Author : Romeo Brunetti
ISBN : 9783319213538
Genre : Science
File Size : 84. 47 MB
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This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

A Mathematical Primer On Quantum Mechanics

Author : Alessandro Teta
ISBN : 9783319778938
Genre : Science
File Size : 77. 92 MB
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This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

Spectral Theory And Its Applications

Author : Bernard Helffer
ISBN : 9781107032309
Genre : Mathematics
File Size : 78. 74 MB
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Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.

From Ordinary To Partial Differential Equations

Author : Giampiero Esposito
ISBN : 9783319575445
Genre : Mathematics
File Size : 22. 27 MB
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This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

Solid State Physics

Author : John J. Quinn
ISBN : 9783319739991
Genre : Science
File Size : 70. 16 MB
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This book provides the basis for a two-semester graduate course on solid-state physics. The first half presents all the knowledge necessary for a one-semester survey of solid-state physics, but in greater depth than most introductory solid state physics courses. The second half includes most of the important research over the past half-century, covering both the fundamental principles and most recent advances. This new edition includes the latest developments in the treatment of strongly interacting two-dimensional electrons and discusses the generalization from small to larger systems. The book provides explanations in a class-tested tutorial style, and each chapter includes problems reviewing key concepts and calculations. The updated exercises and solutions enable students to become familiar with contemporary research activities, such as the electronic properties of massless fermions in graphene and topological insulators.

Inis Atomindex

Author :
ISBN : MINN:31951D00544757R
Genre : Nuclear energy
File Size : 24. 70 MB
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An Introduction To Relativistic Processes And The Standard Model Of Electroweak Interactions

Author : Carlo M. Becchi
ISBN : 9783319061306
Genre : Science
File Size : 49. 42 MB
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This book offers a self-contained introduction to the theory of electroweak interactions based on the semi-classical approach to relativistic quantum field theory, with thorough discussion of key aspects of the field. The basic tools for the calculation of cross sections and decay rates in the context of relativistic quantum field theory are reviewed in a short, but complete and rigorous, presentation. Special attention is focused on relativistic scattering theory and on calculation of amplitude in the semi-classical approximation. The central part of the book is devoted to an illustration of the unified field theory of electromagnetic and weak interactions as a quantum field theory with spontaneously broken gauge invariance; particular emphasis is placed on experimental confirmations of the theory. The closing chapters address the most recent developments in electroweak phenomenology and provide an introduction to the theory and phenomenology of neutrino oscillations. In this 2nd edition the discussion of relativistic scattering processes in the semi-classical approximation has been revised and as a result intermediate results are now explicitly proven. Furthermore, the recent discovery of the Higgs boson is now taken into account throughout the book. In particular, the Higgs decay channel into a pair of photons, which has played a crucial role in the discovery, is discussed. As in the first edition, the accent is still on the semi-classical approximation. However, in view of the necessity of a discussion of H !, the authors give several indications about corrections to the semiclassical approximation. Violation of unitarity is discussed in more detail, including the dispersion relations as a tool for computing loop corrections; the above-mentioned Higgs decay channel is illustrated by means of a full one-loop calculation; and finally, loop effects on the production of unstable particles (such as the Z0 boson) are now discussed. Finally, the neutrino mass and oscillation analysis is updated taking into account the major achievements of the last years.

Enas Aionas Panathinaikos

Author : Aeunaio Eiooioiaeio
ISBN : 1493193775
Genre :
File Size : 53. 57 MB
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Atomic Spectroscopy And Radiative Processes

Author : Egidio Landi Degl'Innocenti
ISBN : 9788847028081
Genre : Science
File Size : 43. 10 MB
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This book describes the basic physical principles of atomic spectroscopy and the absorption and emission of radiation in astrophysical and laboratory plasmas. It summarizes the basics of electromagnetism and thermodynamics and then describes in detail the theory of atomic spectra for complex atoms, with emphasis on astrophysical applications. Both equilibrium and non-equilibrium phenomena in plasmas are considered. The interaction between radiation and matter is described, together with various types of radiation (e.g., cyclotron, synchrotron, bremsstrahlung, Compton). The basic theory of polarization is explained, as is the theory of radiative transfer for astrophysical applications. Atomic Spectroscopy and Radiative Processes bridges the gap between basic books on atomic spectroscopy and the very specialized publications for the advanced researcher: it will provide under- and postgraduates with a clear in-depth description of theoretical aspects, supported by practical examples of applications.

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