The first volume General Theory differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics the content of the book are the lectures of courses actually delivered. It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs.
This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics after a first basic course. With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part Selected Topics are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics.
The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research.
In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics. This text shows that insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics.
It presents the theory of Hermitean operators and Hilbert spaces, providing the framework for transformation theory, and using th. 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. 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. 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, quantum statistics, mean-field theory, second quantization, 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. The last four chapters could also serve as an introductory course in quantum field theory. The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning, which makes it difficult to appreciate the mathematical formalism and understand quantum mechanics.
This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. This book is divided into four parts. Part I is a brief review of the general properties of classical and quantum systems.
A general discussion of probability theory is also included which aims to help in understanding the probability theories relevant to quantum mechanics. Part II is a detailed study of the mathematics for quantum mechanics. Part III presents quantum mechanics in a series of postulates. Six groups of postulates are presented to describe orthodox quantum systems.
Each statement of a postulate is supplemented with a detailed discussion. To make them easier to understand, the postulates for discrete observables are presented before those for continuous observables. Part IV presents several illustrative applications, which include harmonic and isotropic oscillators, charged particle in external magnetic fields and the Aharonov—Bohm effect.
For easy reference, definitions, theorems, examples, comments, properties and results are labelled with section numbers. Various symbols and notations are adopted to distinguish different quantities explicitly and to avoid misrepresentation. Self-contained both mathematically and physically, the book is accessible to a wide readership, including astrophysicists, mathematicians and philosophers of science who are interested in the foundations of quantum mechanics. With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra.
Includes more than problems and 38 figures. IV A bit of algebra: Customers who bought this item also bought. They also sometimes use very elementary fourier analysis, such as the plancherel theorem. This list comes from Takhtajan recommendation of courses needed for the class:. Online Price 1 Label: Print Price 1 Label: Prior to this book, mathematicians could find these topics only mechanlcs physics quantum mechanics for mathematicians takhtajan and in specialized literature.
I think this answer is spot on. An understanding of Borel sets An understanding of manifolds of all jathematicians so a solid Differential Geometry text Should know transforms besides Laplace and Fourier I, also, visited his course website at Stony Brook University and this is what I found. When you click on a Sponsored Product ad, you will be taken to an Amazon detail page where you can learn more about the product and quantum mechanics for mathematicians takhtajan it.
Pages with related products. Amazon Drive Cloud storage from Amazon. Quantum Mechanics for Mathematicians Share this page. Advanced search. Author s Product display : Leon A. Abstract: This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. Volume: Publication Month and Year: Copyright Year: Page Count: Cover Type: Hardcover. Print ISBN Online ISBN Print ISSN: Online ISSN: Primary MSC: Applied Math?
MAA Book?
0コメント