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“…This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. …”
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“…This book provides quick access to quantum mechanics without dealing with a true textbook that demands proper specialized studies in physics (and related mathematics) for about a couple of years. …”
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“…It is a lucid and self-contained introduction to the foundations of quantum mechanics, accessible to anyone with a high school mathematics education, and at the same time a rigorous discussion of the most important recent advances in our understanding of that subject, some of which are due to the author himself.…”
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“…A solid foundation in quantum mechanics and atomic physics is assumed. Early chapters provide background in the mathematical treatment and particular properties of ordinary wave motion that also apply to particle motion. …”
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“…This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. …”
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“…Readers are introduced to the subject through a review of the history of quantum mechanics and an account of classic solutions of the Schrödinger equation, before quantum mechanics is developed in a modern Hilbert space approach. …”
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“…The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the theory. …”
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“…This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. …”
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“…Fundamentals of Quantum Mechanics, Third Edition is a clear and detailed introduction to quantum mechanics and its applications in chemistry and physics. …”
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“…This book highlights the power and elegance of algebraic methods of solving problems in quantum mechanics. It shows that symmetries not only provide elegant solutions to problems that can be solved exactly, but also substantially simplify problems that must be solved approximately. …”
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“…NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS Inadequacy of Classical Description for Small Systems Basis of Quantum Mechanics Representation of States Dual Vectors: Bra and Ket Vectors Linear Operators Adjoint of a Linear Operator Eigenvalues and Eigenvectors of a Linear Operator Physical Interpretation Observables and Completeness Criterion Commutativity and Compatibility of Observables Position and Momentum Commutation Relations Commutation Relation and the Uncertainty ProductAppendix: Basic Concepts in Classical MechanicsREPRESENTATION THEORY Meaning of Representation How to Set up a Representation Representatives of a Linear Operator Change of Representation Coordinate Representation Replacement of Momentum Observable p by -ih d/dqIntegral Representation of Dirac Bracket A2|F|A1> The Momentum Representation Dirac Delta FunctionRelation between the Coordinate and Momentum RepresentationsEQUATIONS OF MOTIONSchrödinger Equation of Motion Schrödinger Equation in the Coordinate Representation Equation of Continuity Stationary States Time-Independent Schrödinger Equation in the Coordinate Representation Time-Independent Schrödinger Equation in the Momentum Representation Time-Independent Schrödinger Equation in Matrix Form The Heisenberg Picture The Interaction Picture Appendix: MatricesPROBLEMS OF ONE-DIMENSIONAL POTENTIAL BARRIERS Motion of a Particle across a Potential Step Passage of a Particle through a Potential Barrier of Finite Extent Tunneling of a Particle through a Potential Barrier Bound States in a One-Dimensional Square Potential Well Motion of a Particle in a Periodic PotentialBOUND STATES OF SIMPLE SYSTEMS Introduction Motion of a Particle in a Box Simple Harmonic Oscillator Operator Formulation of the Simple Harmonic Oscillator Problem Bound State of a Two-Particle System with Central Interaction Bound States of Hydrogen (or Hydrogen-Like) Atoms The Deuteron Problem Energy Levels in a Three-Dimensional Square Well: General Case Energy Levels in an Isotropic Harmonic Potential Well Appendix 1: Special FunctionsAppendix 2: Orthogonal Curvilinear Coordinate SystemsSYMMETRIES AND CONSERVATION LAWS Symmetries and Their Group Properties Symmetries in a Quantum Mechanical System Basic Symmetry Groups of the Hamiltonian and Conservation Laws Lie Groups and Their Generators Examples of Lie Group Appendix 1: Groups and RepresentationsANGULAR MOMENTUM IN QUANTUM MECHANICS Introduction Raising and Lowering Operators Matrix Representation of Angular Momentum Operators Matrix Representation of Eigenstates of Angular Momentum Coordinate Representation of Orbital Angular Momentum Operators and States General Rotation Group and Rotation Matrices Coupling of Two Angular Momenta Properties of Clebsch-Gordan Coefficients Coupling of Three Angular Momenta Coupling of Four Angular Momenta (L - S and j - j Coupling)APPROXIMATION METHODS Introduction Nondegenerate Time-Independent Perturbation Theory Time-Independent Degenerate Perturbation Theory The Zeeman Effect WKBJ Approximation Particle in a Potential Well Application of WKBJ Approximation to a-decay The Variational Method The Problem of the Hydrogen Molecule System of n Identical Particles: Symmetric and Antisymmetric States Excited States of the Helium Atom Statistical (Thomas-Fermi) Model of the Atom Hartree's Self-consistent Field Method for Multi-Electron Atoms Hartree-Fock Equations Occupation Number RepresentationQUANTUM THEORY OF SCATTERING Introduction Laboratory and Center-of-Mass (CM) Reference Frames Scattering Equation and the Scattering AmplitudePartial Waves and Phase Shifts Calculation of Phase Shift Phase Shifts for Some Simple Potential Forms Scattering due to Coulomb Potential The Integral Form of Scattering Equation Lippmann-Schwinger Equation and the Transition Operator Born Expansion Appendix: The Calculus of ResiduesTIME-DEPENDENT PERTURBATION METHODS Introduction Perturbation Constant over an Interval of Time Harmonic Perturbation: Semiclassical Theory of Radiation Einstein Coeffcients Multipole Transitions Electric Dipole Transitions in Atoms and Selection Rules Photo-Electric Effect Sudden and Adiabatic Approximations Second-Order EffectsTHE THREE-BODY PROBLEM Introduction Eyges Approach Mitra's Approach Faddeev's Approach Faddeev Equations in Momentum Representation Faddeev Equations for a Three-Body Bound System Alt, Grassberger, and Sandhas (AGS) EquationsRELATIVISTIC QUANTUM MECHANICS Introduction Dirac Equation Spin of the Electron Free Particle (Plane Wave) Solutions of Dirac Equation Dirac Equation for a Zero Mass Particle Zitterbewegung and Negative Energy Solutions Dirac Equation for an Electron in an Electromagnetic FieldInvariance of Dirac Equation Dirac Bilinear Covariants Dirac Electron in a Spherically Symmetric Potential Charge Conjugation, Parity, and Time-Reversal Invariance Appendix: Theory of Special RelativityQUANTIZATION OF RADIATION FIELD Introduction Radiation Field as a Swarm of Oscillators Quantization of Radiation Field Interaction of Matter with Quantized Radiation Field Applications Bethe's Treatment of Atomic Level Shift Due to the Self Energy of the Electron: (Lamb-Retherford Shift)Compton Scattering Appendix: Electromagnetic Field in Coulomb GaugeSECOND QUANTIZATION Introduction Classical Concept of Field Analogy of Field and Particle Mechanics Field Equations from Lagrangian DensityQuantization of a Real Scalar (KG) Field Quantization of Complex Scalar (KG) Field Dirac Field and Its Quantization Positron Operators and SpinorsInteracting Fields and the Covariant Perturbation Theory Second-Order Processes in Electrodynamics Amplitude for Compton Scattering Feynman Graphs Calculation of the Cross-Section of Compton Scattering Cross-Sections for Other Electromagnetic Processes Appendix 1: Calculus of Variation and Euler-Lagrange Equations Appendix 2: Functionals and Functional Derivatives Appendix 3: Interaction of the Electron and Radiation Fields Appendix 4: On the Convergence of Iterative Expansion of the S OperatorEPILOGUE Introduction Einstein-Podolsky-Rosen Gedanken Experiment Einstein-Podolsky-Rosen-Bohm Gedanken Experiment Theory of Hidden Variables and Bell's Inequality Clauser-Horne Form of Bell's Inequality and Its Violation in Two-Photon Correlation Experiments GENERAL REFERENCESINDEX.…”
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“…HISTORICAL EXPERIMENTS AND THEORIESDates of Important Discoveries and Events Blackbody RadiationPhotoelectrice Effect Quantum Theory of Spectra TheComptone Effect Matterwaves, the de Broglie HypothesisThe Davisson -Germer Experiment Heisenberg's Uncertainity PrincipleDifference Between Particles and Waves Interpretation of the Wavefunction AXIOMATIC STRUCTURE OF QUANTUM MECHANICSThe Necessity of Quantum TheoryFunction Spaces Postulates of Quantum Mechanics The Kronecker Delta and the Dirac Delta Function Dirac Notation OBSERVABLES AND SUPERPOSITIONFree Particle Particle In A Box Ensemble Average Hilbert -Space Interpretation The Initial Square Wave Particle Beam Superposition and Uncertainty Degeneracy of States Commutators and Uncertainty TIME DEVELOPMENT AND CONSERVATION THEOREMSTime Development of State Functions, The Discrete Case The Continuous Case, Wave Packets Particle Beam Gaussian Wave Packet Free Particle Propagator The Limiting Cases of the Gaussian Wave Packets Time Development of Expectation Values Conservation of Energy and MomentumConservation of Parity BOUND AND UNBOUND STATES IN ONE-DIMENSIONOne-Dimensional Schrödinger Equation The Simple Harmonic Oscillator Unbound States One-Dimensional Barrier Problems The Finite Potential Well N-PARTICLE SYSTEMSThe Schrödinger Equation for N-Particle Systems Identical Particles The Pauli Principle; Fermions and Bosons THE SCHRÖDINGER EQUATION IN THREE-DIMENSIONSThe Two-Body Systems Separation of Variables in the Two-Body Systems Rotational Invariance The Schrödinger Equation for Non-Central Potentials ANGULAR MOMENTUMCommutation Relations Raising and Lowering Operators Eigen Solutions of Angular Momentum Operators Kinetic Energy and Angular Momentum THE RADIAL EQUATION FOR FREE AND BOUND PARTICLESThe Radial Schrödinger Equation The Free Particle Three-Dimensional Square Well Potential The Hydrogenatom The Spectra of Hydrogenic Atoms The Virial Theorem INTERACTION OF ELECTRONS WITH ELECTROMAGNETIC FIELDMaxwell 's Equations and Gauge Transformations Motion of a Free Electron in a Uniform Magnetic Field Motion of a Bound Electron in a Uniform Magnetic Field The Principal of Gauge Invariance and Flux Quantization MATRIX REPRESENTATIONSMatrix Representations of Wave Functions and OperatorsMatrix Algebra Types of Matrix Representations Harmonic Oscillator in Matrix Representations Matrix Representations of Angular Momentum Operators SPIN AND THE ADDITION OF ANGULAR MOMENTASystems with Spin One-Half The Addition of Angular Momenta TIME-INDEPENDENT PERTURBATION THEORYNondegenerate Perturbation Theory Degenerate Perturbation Theory THE VARIATIONAL METHODThe Variational Principle Linear Variation Functions THE WKB APPROXIMATION Turning Points The Connection Formulas The WKB Approximation to a Potential Well The WKB Approximation to a Potential Barrier TIME-DEPENDENT PERTURBATION THEORYTime -Dependent Schrödinger Equation Time -Dependent Perturbation Approximations Sinusoidal Perturbations Emission and Absorption of Radiation Incoherent Perturbations Selection RulesTHE ADIABATIC APPROXIMATIONThe Adiabatic Processes The Adiabatic TheoremNonholonomic Processes Experimental Evidences of Nonholonomic Processes PATH-INTEGRATION METHODAn Approximation to Time -Evolution for a Free Particle Path Integral Evaluation of the Free Particle Propagator Equivalence to the Schrödinger Equation SCATTERING THEORYClassical Scattering TheoryCenter-of-Mass and Laboratory Frames Quantum Scattering Theory The Method of Partial waves (Low -Energy Case)Expansion of a Plane Wave into Spherical Waves Expansion of the Scattering Amplitude Scattering from a Delta Potential Scattering from a Square -Well Potential Scattering from a Hardsphere Scattering of Identical Particles Energy Dependence and Resonance Scattering The Lippman-Schwinger Equation (High-Energy Case)The Greens Function for the Scattering Problem Born Approximation INELASTIC SCATTERING Bibliography and References 409Appendix 413Index 417.…”
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