Quantum Mechanics For Mathematicians
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Quantum Theory For Mathematicians
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Author : Brian C. Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-19
Quantum Theory For Mathematicians written by Brian C. Hall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-19 with Science categories.
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.
An Introduction To The Mathematical Structure Of Quantum Mechanics
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Author : F. Strocchi
language : en
Publisher: World Scientific
Release Date : 2005
An Introduction To The Mathematical Structure Of Quantum Mechanics written by F. Strocchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac-Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C--algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems.For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich-Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra.Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman-Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.
Quantum Mechanics For Mathematicians
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Author : Leon Armenovich Takhtadzhi͡an
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Quantum Mechanics For Mathematicians written by Leon Armenovich Takhtadzhi͡an and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Quantum Mechanics For Mathematicians
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Author : Leon Armenovich Takhtadzhi︠a︡n
language : en
Publisher:
Release Date : 1900
Quantum Mechanics For Mathematicians written by Leon Armenovich Takhtadzhi︠a︡n and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1900 with Mathematical physics categories.
Quantum Theory
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Author : Peter Bongaarts
language : en
Publisher: Springer
Release Date : 2014-12-01
Quantum Theory written by Peter Bongaarts and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with Science categories.
This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.
Introduction To The Mathematical Structure Of Quantum Mechanics An A Short Course For Mathematicians
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Author : Franco Strocchi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-11-17
Introduction To The Mathematical Structure Of Quantum Mechanics An A Short Course For Mathematicians written by Franco Strocchi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-17 with Science categories.
This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac-Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C--algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems.For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich-Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra.Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman-Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.
Mathematical Results In Quantum Mechanics
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Author : M. Demuth
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Mathematical Results In Quantum Mechanics written by M. Demuth and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The last decades have demonstrated that quantum mechanics is an inexhaustible source of inspiration for contemporary mathematical physics. Of course, it seems to be hardly surprising if one casts a glance toward the history of the subject; recall the pioneering works of von Neumann, Weyl, Kato and their followers which pushed forward some of the classical mathematical disciplines: functional analysis, differential equations, group theory, etc. On the other hand, the evident powerful feedback changed the face of the "naive" quantum physics. It created a contem porary quantum mechanics, the mathematical problems of which now constitute the backbone of mathematical physics. The mathematical and physical aspects of these problems cannot be separated, even if one may not share the opinion of Hilbert who rigorously denied differences between pure and applied mathemat ics, and the fruitful oscilllation between the two creates a powerful stimulus for development of mathematical physics. The International Conference on Mathematical Results in Quantum Mechan ics, held in Blossin (near Berlin), May 17-21, 1993, was the fifth in the series of meetings started in Dubna (in the former USSR) in 1987, which were dedicated to mathematical problems of quantum mechanics. A primary motivation of any meeting is certainly to facilitate an exchange of ideas, but there also other goals. The first meeting and those that followed (Dubna, 1988; Dubna, 1989; Liblice (in the Czech Republic), 1990) were aimed, in particular, at paving ways to East-West contacts.
Quantum Mathematical Physics
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Author : Felix Finster
language : en
Publisher: Birkhäuser
Release Date : 2016-02-24
Quantum Mathematical Physics written by Felix Finster and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-24 with Science categories.
Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.
Quantum Field Theory A Tourist Guide For Mathematicians
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Author : Gerald B. Folland
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-02-03
Quantum Field Theory A Tourist Guide For Mathematicians written by Gerald B. Folland and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-03 with Education categories.
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam–Weinberg model of electromagnetic and weak interactions.
Supersymmetry For Mathematicians An Introduction
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Author : V. S. Varadarajan
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Supersymmetry For Mathematicians An Introduction written by V. S. Varadarajan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
An special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity."--Jacket.