Quantum Theory for Mathematicians

Quantum Theory for Mathematicians
Author :
Publisher : Springer Science & Business Media
Total Pages : 566
Release :
ISBN-10 : 9781461471165
ISBN-13 : 1461471168
Rating : 4/5 (65 Downloads)

Synopsis Quantum Theory for Mathematicians by : Brian C. Hall

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.

Quantum Mechanics for Mathematicians

Quantum Mechanics for Mathematicians
Author :
Publisher : American Mathematical Soc.
Total Pages : 410
Release :
ISBN-10 : 9780821846308
ISBN-13 : 0821846302
Rating : 4/5 (08 Downloads)

Synopsis Quantum Mechanics for Mathematicians by : Leon Armenovich Takhtadzhi͡an

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.

Lectures on Quantum Mechanics for Mathematics Students

Lectures on Quantum Mechanics for Mathematics Students
Author :
Publisher : American Mathematical Soc.
Total Pages : 250
Release :
ISBN-10 : 9780821846995
ISBN-13 : 082184699X
Rating : 4/5 (95 Downloads)

Synopsis Lectures on Quantum Mechanics for Mathematics Students by : L. D. Faddeev

Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.

Mathematical Methods in Quantum Mechanics

Mathematical Methods in Quantum Mechanics
Author :
Publisher : American Mathematical Soc.
Total Pages : 322
Release :
ISBN-10 : 9780821846605
ISBN-13 : 0821846604
Rating : 4/5 (05 Downloads)

Synopsis Mathematical Methods in Quantum Mechanics by : Gerald Teschl

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).

Quantum Field Theory: A Tourist Guide for Mathematicians

Quantum Field Theory: A Tourist Guide for Mathematicians
Author :
Publisher : American Mathematical Soc.
Total Pages : 325
Release :
ISBN-10 : 9781470464837
ISBN-13 : 1470464837
Rating : 4/5 (37 Downloads)

Synopsis Quantum Field Theory: A Tourist Guide for Mathematicians by : Gerald B. Folland

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.

Lectures on Quantum Mechanics

Lectures on Quantum Mechanics
Author :
Publisher : Cambridge University Press
Total Pages : 585
Release :
ISBN-10 : 9781108429764
ISBN-13 : 1108429769
Rating : 4/5 (64 Downloads)

Synopsis Lectures on Quantum Mechanics by : Philip L. Bowers

A leisurely but mathematically honest presentation of quantum mechanics for graduate students in mathematics with an interest in physics.

The Mathematical Principles of Quantum Mechanics

The Mathematical Principles of Quantum Mechanics
Author :
Publisher : Courier Corporation
Total Pages : 306
Release :
ISBN-10 : 9780486442235
ISBN-13 : 0486442233
Rating : 4/5 (35 Downloads)

Synopsis The Mathematical Principles of Quantum Mechanics by : Derek F. Lawden

Focusing on the principles of quantum mechanics, this text for upper-level undergraduates and graduate students introduces and resolves special physical problems with more than 100 exercises. 1967 edition.

Mathematical Foundations of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics
Author :
Publisher : Princeton University Press
Total Pages : 462
Release :
ISBN-10 : 0691028931
ISBN-13 : 9780691028934
Rating : 4/5 (31 Downloads)

Synopsis Mathematical Foundations of Quantum Mechanics by : John von Neumann

A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books

A Mathematical Primer on Quantum Mechanics

A Mathematical Primer on Quantum Mechanics
Author :
Publisher : Springer
Total Pages : 265
Release :
ISBN-10 : 9783319778938
ISBN-13 : 3319778935
Rating : 4/5 (38 Downloads)

Synopsis A Mathematical Primer on Quantum Mechanics by : Alessandro Teta

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.

Physics for Mathematicians

Physics for Mathematicians
Author :
Publisher :
Total Pages : 733
Release :
ISBN-10 : 0914098322
ISBN-13 : 9780914098324
Rating : 4/5 (22 Downloads)

Synopsis Physics for Mathematicians by : Michael Spivak