Concepts in Quantum Mechanics
CRC Press (Verlag)
978-1-138-58276-7 (ISBN)
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The authors present alternative ways of representing the state of a physical system, outline the mathematical connection between the representatives of the same state in different representations, and highlight the connection between Dirac brackets and their integral forms in the coordinate and momentum representations. They also logically develop the equations of motion in Schrödinger and Heisenberg pictures. In addition, the book covers motion in the presence of potential steps and wells, bound state problems, symmetries and their consequences, the role of angular momentum in quantum mechanics, approximation methods, time-dependent perturbation methods, and second quantization.
Written by authoritative professors who have taught quantum mechanics at the graduate level for a combined forty years, this textbook provides students with a strong foundation in quantum mechanics. After reading the book, students will be ready to take on quantum field theory.
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 Product
Appendix: Basic Concepts in Classical Mechanics
REPRESENTATION 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/dq
Integral Representation of Dirac Bracket
The Momentum Representation
Dirac Delta Function
Relation between the Coordinate and Momentum Representations
EQUATIONS OF MOTION
Schrödinger 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: Matrices
PROBLEMS 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 Potential
BOUND 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 Functions
Appendix 2: Orthogonal Curvilinear Coordinate Systems
SYMMETRIES 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 Representations
ANGULAR 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 Representation
QUANTUM THEORY OF SCATTERING
Introduction
Laboratory and Center-of-Mass (CM) Reference Frames
Scattering Equation and the Scattering Amplitude
Partial 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 Residues
TIME-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 Effects
THE 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) Equations
RELATIVISTIC 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 Field
Invariance of Dirac Equation
Dirac Bilinear Covariants
Dirac Electron in a Spherically Symmetric Potential
Charge Conjugation, Parity, and Time-Reversal Invariance
Appendix: Theory of Special Relativity
QUANTIZATION 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 Gauge
SECOND QUANTIZATION
Introduction
Classical Concept of Field
Analogy of Field and Particle Mechanics
Field Equations from Lagrangian Density
Quantization of a Real Scalar (KG) Field
Quantization of Complex Scalar (KG) Field
Dirac Field and Its Quantization
Positron Operators and Spinors
Interacting 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 Operator
EPILOGUE
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 REFERENCES
INDEX
| Erscheint lt. Verlag | 31.12.2023 |
|---|---|
| Reihe/Serie | Pure and Applied Physics |
| Zusatzinfo | 3 Tables, black and white; 107 Illustrations, black and white |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| ISBN-10 | 1-138-58276-X / 113858276X |
| ISBN-13 | 978-1-138-58276-7 / 9781138582767 |
| Zustand | Neuware |
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