Mathematical Methods In Quantum Mechanics

Author : Gerald Teschl
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 46,7 Mb
Release : 2009
Category : Quantum theory
ISBN : 9780821846605

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Mathematical Methods in Quantum Mechanics by Gerald Teschl Pdf

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).

Author : Philippe Blanchard,Erwin Bruening
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200499

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Mathematical Methods in Physics by Philippe Blanchard,Erwin Bruening Pdf

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Author : Detlef Lehmann
Publisher : CRC Press
Page : 264 pages
File Size : 48,6 Mb
Release : 2004-08-30
Category : Mathematics
ISBN : 9781482286052

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Mathematical Methods of Many-Body Quantum Field Theory by Detlef Lehmann Pdf

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theo

Author : Ravinder R. Puri
Publisher : Springer
Page : 291 pages
File Size : 47,7 Mb
Release : 2012-11-02
Category : Science
ISBN : 9783540449539

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Mathematical Methods of Quantum Optics by Ravinder R. Puri Pdf

Starting from first principles, this reference treats the theoretical aspects of quantum optics. It develops a unified approach for determining the dynamics of a two-level and three-level atom in combinations of quantized field under certain conditions.

Author : Martin Schechter
Publisher : Courier Corporation
Page : 350 pages
File Size : 53,6 Mb
Release : 2014-06-10
Category : Science
ISBN : 9780486150048

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Operator Methods in Quantum Mechanics by Martin Schechter Pdf

This text introduces techniques related to physical theory. Entire book is devoted to a particle moving in a straight line; students develop techniques by answering questions about the particle. 1981 edition.

Author : Frederick W. Byron,Robert W. Fuller
Publisher : Courier Corporation
Page : 674 pages
File Size : 51,8 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486135069

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Mathematics of Classical and Quantum Physics by Frederick W. Byron,Robert W. Fuller Pdf

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Author : STEPHEN J. GUSTAFSON
Publisher : Unknown
Page : 128 pages
File Size : 53,9 Mb
Release : 2020
Category : Mathematics
ISBN : 9783030595623

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MATHEMATICAL CONCEPTS OF QUANTUM MECHANICS by STEPHEN J. GUSTAFSON Pdf

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.

Author : H. W. Wyld
Publisher : CRC Press
Page : 296 pages
File Size : 46,5 Mb
Release : 2018-03-14
Category : Science
ISBN : 9780429978647

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Mathematical Methods For Physics by H. W. Wyld Pdf

This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, one-sided Fourier transforms, and Laplace transforms.

Author : Alessandro Teta
Publisher : Springer
Page : 265 pages
File Size : 41,5 Mb
Release : 2018-04-17
Category : Science
ISBN : 9783319778938

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A Mathematical Primer on Quantum Mechanics by Alessandro Teta Pdf

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.

Author : Tulsi Dass,S.K. Sharma
Publisher : Universities Press
Page : 718 pages
File Size : 53,7 Mb
Release : 1998
Category : Mathematical physics
ISBN : 8173710899

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Mathematical Methods In Classical And Quantum Physics by Tulsi Dass,S.K. Sharma Pdf

This book is intended to provide an adequate background for various theortical physics courses, especially those in classical mechanics, electrodynamics, quatum mechanics and statistical physics. Each topic is dealt with in a generally self-contained manner and the text is interspersed with a number of solved examples ad a large number of exercise problems.

Author : Gerald Teschl
Publisher : Unknown
Page : 322 pages
File Size : 47,7 Mb
Release : 2009
Category : Quantum theory
ISBN : 147041838X

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Mathematical Methods in Quantum Mechanics by Gerald Teschl Pdf

Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 55,9 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9781475720631

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Mathematical Methods of Classical Mechanics by V.I. Arnol'd Pdf

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Author : Brian C. Hall
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 48,9 Mb
Release : 2013-06-19
Category : Science
ISBN : 9781461471165

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Quantum Theory for Mathematicians by Brian C. Hall Pdf

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

Author : Leon Armenovich Takhtadzhi͡an
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 47,9 Mb
Release : 2008
Category : Mathematical physics
ISBN : 9780821846308

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Quantum Mechanics for Mathematicians by Leon Armenovich Takhtadzhi͡an Pdf

Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.

Author : Fabio Bagarello,Jean-Pierre Gazeau,Franciszek Hugon Szafraniec,Miloslav Znojil
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 45,7 Mb
Release : 2015-09-09
Category : Science
ISBN : 9781118855270

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Non-Selfadjoint Operators in Quantum Physics by Fabio Bagarello,Jean-Pierre Gazeau,Franciszek Hugon Szafraniec,Miloslav Znojil Pdf

A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.