Supersymmetric Quantum Mechanics

Author: Asim Gangopadhyaya
Editor: World Scientific Publishing Company
ISBN: 9813221062
File Size: 52,17 MB
Format: PDF, Docs
Read: 2891
Download

We have written this book in order to provide a single compact source for undergraduate and graduate students, as well as for professional physicists who want to understand the essentials of supersymmetric quantum mechanics. It is an outgrowth of a seminar course taught to physics and mathematics juniors and seniors at Loyola University Chicago, and of our own research over a quarter of a century.

Supersymmetry In Quantum Mechanics

Author: Fred Cooper
Editor: World Scientific
ISBN: 9814491144
File Size: 80,76 MB
Format: PDF
Read: 129
Download

This invaluable book provides an elementary description of supersymmetric quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. It gives physicists a fresh outlook and new ways of handling quantum-mechanical problems, and also leads to improved approximation techniques for dealing with potentials of interest in all branches of physics. The algebraic approach to obtaining eigenstates is elegant and important, and all physicists should become familiar with this. The book has been written in such a way that it can be easily appreciated by students in advanced undergraduate quantum mechanics courses. Problems have been given at the end of each chapter, along with complete solutions to all the problems. The text also includes material of interest in current research not usually discussed in traditional courses on quantum mechanics, such as the connection between exact solutions to classical soliton problems and isospectral quantum Hamiltonians, and the relation to the inverse scattering problem. Contents:The Schrödinger Equation in One DimensionFactorization of a General HamiltonianShape Invariance and Solvable PotentialsCharged Particles in External Fields and SupersymmetryIsospectral HamiltoniansNew Periodic Potentials from SupersymmetrySupersymmetric WKB ApproximationPerturbative Methods for Calculating Energy Spectra and Wave FunctionsAppendices:Path Integrals and SUSYOperator Transforms — New Solvable Potentials from OldLogarithmic Perturbation TheorySolutions to Problems Readership: Graduate and advanced undergraduate students and researchers in quantum, mathematical, theoretical and high energy physics. Keywords:Supersymmetric Quantum Mechanics;Quantum Mechanics;Shape Invariant Potentials;Factorization of Hamiltonian;Solvable Potentials;Isospectral Hamiltonians;Periodic Potentials;Supersymmetric WKB Approximation;Path Integrals and Supersymmetry;Supersymmetry and Dirac Equation;Unbroken Supersymmetry;Broken Supersymmetry;Logarithmic Perturbation TheoryReviews:“The many figures and exercises with answers make this book particularly suitable for students in advanced undergraduate and beginning graduate quantum-mechanical courses.”Mathematics Abstracts “… this eminently readable book is a welcome introductory treatise on supersymmetric methods in quantum mechanics … the elementary mathematical language employed throughout the book makes it accessible to anybody who has gone through an introductory quantum mechanics course.”Mathematical Reviews “It provides a solid basic background to some important and deep ideas in quantum mechanics which also have applications in quantum field theory. The authors have kept the discussion simple and clear, but have nevertheless managed to capture much of the beauty and richness of the subject. I think most readers will come to the end of the book having learned many things, and being eager to know more about the subject of supersymmetry. In this sense the book is a success — it whets the appetite and conveys a taste of the magic of supersymmetry.”Contemporary Physics “The authors of this monograph have made significance contributions to this field, especially those related to systematics of shape invariant potentials, new exact models of band structure and WKB approximation. They have produced a delightful monograph on the subject. The usefulness of this monograph is further enhanced by a set of exercises given with each chapter.”Current Science “After a semester of undergraduate quantum mechanics, a student could read the first three chapters and have no difficulty grasping the meaning of supersymmetry. Depending on interest, an instructor could select special topics in this book for unusual twists on quantum mechanics problems … someone studying supersymmetric field theory is likely to find this book helpful to illustrate complex ideas through simpler examples.”American Journal of Physics

Supersymmetric Methods In Quantum And Statistical Physics

Author: Georg Junker
Editor: Springer Science & Business Media
ISBN: 364261194X
File Size: 21,94 MB
Format: PDF, Docs
Read: 7944
Download

The idea of supersymmetry was originally introduced in relativistic quantum field theories as a generalization of Poincare symmetry. In 1976 Nicolai sug gested an analogous generalization for non-relativistic quantum mechanics. With the one-dimensional model introduced by Witten in 1981, supersym metry became a major tool in quantum mechanics and mathematical, sta tistical, and condensed-IIll;l. tter physics. Supersymmetry is also a successful concept in nuclear and atomic physics. An underlying supersymmetry of a given quantum-mechanical system can be utilized to analyze the properties of the system in an elegant and effective way. It is even possible to obtain exact results thanks to supersymmetry. The purpose of this book is to give an introduction to supersymmet ric quantum mechanics and review some of the recent developments of vari ous supersymmetric methods in quantum and statistical physics. Thereby we will touch upon some topics related to mathematical and condensed-matter physics. A discussion of supersymmetry in atomic and nuclear physics is omit ted. However, the reader will find some references in Chap. 9. Similarly, super symmetric field theories and supergravity are not considered in this book. In fact, there exist already many excellent textbooks and monographs on these topics. A list may be found in Chap. 9. Yet, it is hoped that this book may be useful in preparing a footing for a study of supersymmetric theories in atomic, nuclear, and particle physics. The plan of the book is as follows.

An Introduction To Symmetry And Supersymmetry In Quantum Field Theory

Author: Jan T. ?opusza?ski
Editor: World Scientific
ISBN: 9789971501617
File Size: 27,70 MB
Format: PDF, ePub
Read: 8582
Download

This is a set of lecture notes given by the author at the Universities of G”ttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics.

Introduction To Quantum Mechanics

Author: Sy M. Blinder
Editor: Elsevier
ISBN: 0080489281
File Size: 16,34 MB
Format: PDF, ePub
Read: 9952
Download

Introduction to Quantum Mechanics provides a lucid, up-to-date introduction to the principles of quantum mechanics at the level of undergraduates and first-year graduate students in chemistry, materials science, biology and related fields. It shows how the fundamental concepts of quantum theory arose from classic experiments in physics and chemistry, and presents the quantum-mechanical foundations of modern techniques including molecular spectroscopy, lasers and NMR. Blinder also discusses recent conceptual developments in quantum theory, including Schrödinger's Cat, the Einstein-Podolsky-Rosen experiment, Bell's theorem and quantum computing. Clearly presents the basics of quantum mechanics and modern developments in the field Explains applications to molecular spectroscopy, lasers, NMR, and MRI Introduces new concepts such as Schrödinger's Cat, Bell's Theorem, and quantum computing Includes full-color illustrations, proven pedagogical features, and links to online materials

Introduction To Quantum Mechanics

Author: S. M. Blinder
Editor: Academic Press
ISBN: 0128223111
File Size: 52,73 MB
Format: PDF
Read: 2905
Download

Introduction to Quantum Mechanics, Second Edition presents an accessible, fully-updated introduction on the principles of quantum mechanics. The book outlines the fundamental concepts of quantum theory, discusses how these arose from classic experiments in chemistry and physics, and presents the quantum-mechanical foundations of many key scientific techniques. Chapters cover an introduction to the key principles underpinning quantum mechanics, differing types of molecular structures, bonds and behaviors, and applications of quantum mechanical theory across a number of important fields, including new chapters on Density Functional Theory, Statistical Thermodynamics and Quantum Computing. Drawing on the extensive experience of its expert author, this book is a reliable introduction to the principles of quantum mechanics for anyone new to the field, and a useful refresher on fundamental knowledge and latest developments for anyone more experienced in the field. Presents a fully updated accounting that reflects the most recent developments in Quantum Theory and its applications Includes new chapters on Special Functions, Density Functional Theory, Statistical Thermodynamics and Quantum Computers Presents additional problems and exercises to further support learning

Supersymmetric Methods In Quantum Statistical And Solid State Physics

Author: Georg Junker
Editor:
ISBN: 9780750320269
File Size: 80,21 MB
Format: PDF, ePub, Mobi
Read: 5149
Download

As with the earlier edition, this book provides an accessible introduction to supersymmetric quantum mechanics and its applications in quantum, statistical and solid state physics. Building on the earlier edition it now encapsulates the substantial developments that have been made in supersymmetric quantum mechanics in recent years including conditionally exactly solvable systems, models of classical field theory and the many new interesting aspects within the area of stochastic dynamics, the Pauli and Dirac Equation, coherent states and non-linear algebras. Aimed at graduate students and scientists this book provides a thorough review on supersymmetric quantum mechanics and now includes problems and solutions.

Planar Supersymmetric Quantum Mechanics Of A Charged Particle In An External Electromagnetic Field

Author: Ricardo C. Paschoal
Editor:
ISBN:
File Size: 49,52 MB
Format: PDF, ePub
Read: 8782
Download


The Quantum Theory Of Fields

Author: Steven Weinberg
Editor: Cambridge University Press
ISBN: 9780521660006
File Size: 52,81 MB
Format: PDF, Docs
Read: 3146
Download

In this third volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This volume presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, non-perturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, including previously unpublished results. Exercises are included.

Classification Of Irreps And Invariants Of The N Extended Supersymmetric Quantum Mechanics

Author: Zhanna Kuznetsova
Editor:
ISBN:
File Size: 54,93 MB
Format: PDF, ePub
Read: 484
Download


Instantons And Large N

Author: Marcos Mariño
Editor: Cambridge University Press
ISBN: 1316368548
File Size: 32,11 MB
Format: PDF
Read: 9726
Download

This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang–Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behavior of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.

Symmetries In Quantum Mechanics

Author: M Chaichian
Editor: CRC Press
ISBN: 9780750304085
File Size: 54,24 MB
Format: PDF
Read: 6744
Download

Symmetries in Quantum Mechanics: From Angular Momentum to Supersymmetry (PBK) provides a thorough, didactic exposition of the role of symmetry, particularly rotational symmetry, in quantum mechanics. The bulk of the book covers the description of rotations (geometrically and group-theoretically) and their representations, and the quantum theory of angular momentum. Later chapters introduce more advanced topics such as relativistic theory, supersymmetry, anyons, fractional spin, and statistics. With clear, in-depth explanations, the book is ideal for use as a course text for postgraduate and advanced undergraduate students in physics and those specializing in theoretical physics. It is also useful for researchers looking for an accessible introduction to this important area of quantum theory.

Decomposition And Oxidation Of The N Extended Supersymmetric Quantum Mechanics Multiplets

Author: Zhanna Kuznetsova
Editor:
ISBN:
File Size: 22,20 MB
Format: PDF, Mobi
Read: 5359
Download


Quantum Field Theory

Author: Lewis H. Ryder
Editor: Cambridge University Press
ISBN: 9780521478144
File Size: 46,30 MB
Format: PDF, ePub, Docs
Read: 8864
Download

This book is a modern introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the author develops the quantum theory of scalar and spinor fields, and then of gauge fields. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of "topological" objects in field theory and, new to this edition, a chapter devoted to supersymmetry. Graduate students in particle physics and high energy physics will benefit from this book.

The Supersymmetric Dirac Equation

Author: Allen Hirshfeld
Editor: World Scientific
ISBN: 1848167970
File Size: 41,90 MB
Format: PDF, ePub, Docs
Read: 5551
Download

The solution of the Dirac equation for an electron in a Coulomb field is systematically treated here by utilizing new insights provided by supersymmetry. It is shown that each of the concepts has its analogue in the non-relativistic case. Indeed, the non-relativistic case is developed first, in order to introduce the new concepts in a familiar context. The symmetry of the non-relativistic model is already present in the classical limit, so the classical Kepler problem is first discussed in order to bring out the role played by the Laplace vector, one of the central concepts of the whole book. Analysis of the concept of eccentricity of the orbits turns out to be essential to understanding the relation of the classical and quantum mechanical models. The opportunity is taken to relive the great moments of physics: From Kepler's discovery of the laws of motion of the planets the development is traced through the Dirac equation up to modern advances, which bring the concepts of supersymmetry to bear on the derivation of the solutions.

Path Integrals And Anomalies In Curved Space

Author: Fiorenzo Bastianelli
Editor: Cambridge University Press
ISBN: 1139456849
File Size: 48,98 MB
Format: PDF, Kindle
Read: 4624
Download

Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. The authors start by deriving path integrals for particles moving in curved space and their supersymmetric generalizations. They then discuss the regularization schemes essential to constructing and computing these path integrals. This topic is used to introduce regularization and renormalization in quantum field theories in a wider context. These methods are then applied to discuss and calculate anomalies in quantum field theory. Such anomalies provide enormous constraints in the search for physical theories of elementary particles, quantum gravity and string theories. An advanced text for researchers and graduate students of quantum field theory and string theory, the first part is also a stand-alone introduction to path integrals in quantum mechanics.

Supersymmetry For Mathematicians An Introduction

Author: V. S. Varadarajan
Editor: American Mathematical Soc.
ISBN: 9780821883518
File Size: 56,27 MB
Format: PDF, ePub
Read: 392
Download

Supersymmetry has been the object of study by theoretical physicists since the early 1970's. In recent years it has attracted the interest of mathematicians because of its novelty, and because of significance, both in mathematics and physics, of the main issues it raises. This book presents the foundations of supersymmetry to the mathematically minded reader in a cogent and self-contained manner. It begins with a brief introduction to the physical foundations of the theory, especially the classification of relativistic particles and their wave equations, such as the equations of Dirac and Weyl. It then continues the development of the theory of supermanifolds stressing the analogy with the Grothendieck theory of schemes. All the super linear algebra needed for the book is developed here and the basic theorems are established: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on. A 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.

Quantum Mechanics

Author: K.T. Hecht
Editor: Springer Science & Business Media
ISBN: 1461212723
File Size: 20,74 MB
Format: PDF, ePub, Docs
Read: 2849
Download

Intended for beginning graduate students, this text takes the reader from the familiar coordinate representation of quantum mechanics to the modern algebraic approach, emphasizing symmetry principles throughout. After an introduction to the basic postulates and techniques, the book discusses time-independent perturbation theory, angular momentum, identical particles, scatteering theory, and time-dependent perturbation theory. The whole is rounded off with several lectures on relativistic quantum mechanics and on many-body theory.

Quantum Field Theory

Author: Michio Kaku
Editor: Oxford University Press on Demand
ISBN: 9780195076523
File Size: 28,68 MB
Format: PDF, Mobi
Read: 2168
Download

Provides a comprehensive discussion of the gauge revolution and the theoretical and experimental evidence which makes the Standard Model the leading theory of subatomic phenomena.