Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics

Author : Gianfausto Dell'Antonio
Publisher : Springer
Page : 381 pages
File Size : 43,6 Mb
Release : 2016-05-24
Category : Science
ISBN : 9789462391154

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Lectures on the Mathematics of Quantum Mechanics II: Selected Topics by Gianfausto Dell'Antonio Pdf

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.

Author : Gianfausto Dell'Antonio
Publisher : Atlantis Press
Page : 459 pages
File Size : 51,8 Mb
Release : 2015-06-09
Category : Science
ISBN : 9462391173

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Lectures on the Mathematics of Quantum Mechanics I by Gianfausto Dell'Antonio Pdf

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.

Author : L. D. Faddeev,Oleg Aleksandrovich I︠A︡kubovskiĭ
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 42,9 Mb
Release : 2009
Category : Quantum theory
ISBN : 9780821846995

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Lectures on Quantum Mechanics for Mathematics Students by L. D. Faddeev,Oleg Aleksandrovich I︠A︡kubovskiĭ Pdf

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.

Author : Matteo Gallone,Alessandro Michelangeli
Publisher : Springer Nature
Page : 557 pages
File Size : 43,9 Mb
Release : 2023-04-04
Category : Science
ISBN : 9783031108853

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Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians by Matteo Gallone,Alessandro Michelangeli Pdf

This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac–Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.

Author : Isham Chris J
Publisher : World Scientific
Page : 276 pages
File Size : 42,6 Mb
Release : 1995-09-01
Category : Science
ISBN : 9781911298021

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Lectures On Quantum Theory: Mathematical And Structural Foundations by Isham Chris J Pdf

This book is based on material taught to final-year physics undergraduates as part of the theoretical physics option at Imperial College. After a self-contained introduction to the essential ideas of vector spaces and linear operators, a bridge is built between the concepts and mathematics of classical physics, and the new mathematical framework employed in quantum mechanics. The axioms of nonrelativistic quantum theory are introduced, and shown to lead to a variety of new conceptual problems. Subjects discussed include state-vector reduction, the problem of measurement, quantum entanglement, the Kochen-Specker theorem, and the Bell inequalities. The book includes twenty-five problems with worked solutions.

Author : Paul A. M. Dirac
Publisher : Courier Corporation
Page : 96 pages
File Size : 54,6 Mb
Release : 2013-05-27
Category : Science
ISBN : 9780486320281

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Lectures on Quantum Mechanics by Paul A. M. Dirac Pdf

Four concise, brilliant lectures on mathematical methods in quantum mechanics from Nobel Prize–winning quantum pioneer build on idea of visualizing quantum theory through the use of classical mechanics.

Author : F. Strocchi
Publisher : World Scientific
Page : 194 pages
File Size : 50,5 Mb
Release : 1993
Category : Science
ISBN : 981021149X

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Selected Topics on the General Properties of Quantum Field Theory by F. Strocchi Pdf

This book provides a readable account of the foundations of QFT, in particular of the Euclidean formulation with emphasis on the interplay between physical requirements and mathematical structures. The general structures underlying the conventional local (renormalizable) formulation of gauge QFT are discussed also on the basis of simple models. The mechanism of confinement, non-trivial topology and ?-vacua, chiral symmetry breaking and solution of the U(1) problem are clarified through a careful analysis of the Schwinger model, which settles unclear or debated points.

Author : Philip L. Bowers
Publisher : Cambridge University Press
Page : 585 pages
File Size : 47,5 Mb
Release : 2020-09-17
Category : Science
ISBN : 9781108429764

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Lectures on Quantum Mechanics by Philip L. Bowers Pdf

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

Author : Gianfausto Dell'Antonio
Publisher : Unknown
Page : 128 pages
File Size : 47,5 Mb
Release : 2015
Category : Electronic
ISBN : OCLC:1074987176

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Lectures on the Mathematics of Quantum Mechanics by Gianfausto Dell'Antonio Pdf

Author : Oliver Bühler
Publisher : American Mathematical Soc.
Page : 165 pages
File Size : 42,9 Mb
Release : 2006-10-12
Category : Mathematical physics
ISBN : 9780821842324

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A Brief Introduction to Classical, Statistical, and Quantum Mechanics by Oliver Bühler Pdf

This book provides a rapid overview of the basic methods and concepts in mechanics for beginning Ph.D. students and advanced undergraduates in applied mathematics or related fields. It is based on a graduate course given in 2006-07 at the Courant Institute of Mathematical Sciences. Among other topics, the book introduces Newton's law, action principles, Hamilton-Jacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum path-integral methods. The focus is on fundamental mathematical methods that provide connections between seemingly unrelated subjects. An example is Hamilton-Jacobi theory, which appears in the calculus of variations, in Fermat's principle of classical mechanics, and in the geometric theory of dispersive wavetrains. The material is developed in a sequence of simple examples and the book can be used in a one-semester class on classical, statistical, and quantum mechanics. Some familiarity with differential equations is required but otherwise the book is self-contained. In particular, no previous knowledge of physics is assumed. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Author : Joel S. Feldman,Richard Gerd Froese,Lon M. Rosen
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 51,5 Mb
Release : 1995
Category : Science
ISBN : 9780821803660

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Mathematical Quantum Theory II: Schrodinger Operators by Joel S. Feldman,Richard Gerd Froese,Lon M. Rosen Pdf

The articles in this collection constitute the proceedings of the Canadian Mathematical Society Annual Seminar on Mathematical Quantum Theory, held in Vancouver in August 1993. The meeting was run as a research-level summer school concentrating on two related areas of contemporary mathematical physics. The first area, quantum field theory and many-body theory, is covered in volume 1 of these proceedings. The second area, treated in the present volume, is Schrödinger operators. The meeting featured a series of four-hour mini-courses, designed to introduce students to the state of the art in particular areas, and thirty hour-long expository lectures. With contributions from some of the top experts in the field, this book is an important resource for those interested in activity at the frontiers of mathematical quantum theory.

Author : Floyd Williams
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200093

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Topics in Quantum Mechanics by Floyd Williams Pdf

This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.

Author : William A. Schwalm
Publisher : Morgan & Claypool Publishers
Page : 86 pages
File Size : 54,7 Mb
Release : 2017-05-02
Category : Science
ISBN : 9781681744490

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Lectures on Selected Topics in Mathematical Physics by William A. Schwalm Pdf

This book provides an introduction to Lie Theory for first year graduate students and professional physicists who may not have across the theory in their studies. In particular, it is a summary overview of the theory of finite groups, a brief description of a manifold, and then an informal development of the theory of one-parameter Lie groups, especially as they apply to ordinary differential equations. The treatment is informal, but systematic and reasonably self-contained, as it assumes a familiarity with basic physics and applied calculus, but it does not assume additional mathematical training. Interested readers should have a fair chance of finding symmetries of a second order differential equation and should be able to use it to reduce the order of the differential equation.

Author : Gianfausto Dell'Antonio
Publisher : Springer
Page : 459 pages
File Size : 43,7 Mb
Release : 2015-05-25
Category : Science
ISBN : 9789462391185

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Lectures on the Mathematics of Quantum Mechanics I by Gianfausto Dell'Antonio Pdf

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.

Author : Gregor Wentzel,S. M. Vaidya
Publisher : Unknown
Page : 306 pages
File Size : 51,5 Mb
Release : 1965
Category : Quantum theory
ISBN : UOM:39015015980785

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Lectures on Special Topics in Quantum Mechanics by Gregor Wentzel,S. M. Vaidya Pdf