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Interaction of Photons and Neutrons With Matter: An Introduction

Sow‐Hsin Chen, Michael Kotlarchyk

Published Mar 9, 2007• 5 citations
OpenAlex

Abstract

An overview of classical mechanics the transition to quantum mechanics classical treatment of electromagnetic fields and radiation quantum properties of the field time-dependent perturbation theory, transition probabilities and scattering the density operator and its role in quantum statistics first-order radiation processes second-order processes and the scattering of photons principles of nuclear magnetic resonance. (Part Contents).

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Interactions of Photons and Neutrons with Matter

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Heisenberg's Quantum Mechanics

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Quantum Mechanics: An Accessible Introduction

Robert J. Scherrer

Table of Contents 1. The Origins of Quantum Mechanics 1.1 Introduction 1.2 Blackbody Radiation The Problem with Blackbody Radiation 1.3 The Nature of Light The Photoelectric Effect The Compton Effect Is it a Particle or a Wave? 1.4 TheWave Nature of Matter 1.5 The Bohr Atom 1.6 Where do we Stand? 2. Math Interlude A: Complex Numbers and Linear Operators 2.1 Complex Numbers 2.2 Operators Definition of an Operator Eigenfunctions and Eigenvalues 3. The Schrodinger Equation 3.1 Derivation of the Schrodinger Equation 3.2 The Meaning of theWave Function 3.3 The Time-Independent Schrodinger Equation Derivation of the Time-Independent Schrodinger Equation Qualitative Solutions and the Origin of Quantization 4. One-Dimensional Time-Independent Schrodinger Equation 4.1 Unbound States: Scattering and Tunneling Scattering From Step-Function Potentials 4.2 Bound Systems The Infinite SquareWell The Harmonic Oscillator Potential 5. Math Interlude B: Linear Algebra 5.1 Properties of Linear Operators 5.2 Vector Spaces Inner Products Adjoint and Hermitian Operators Basis Sets 6. The Three-Dimensional Time-Independent Schrodinger Equation 6.1 Solution in Rectangular Coordinates 6.2 Angular Momentum 6.3 The Schrodinger Equation in Spherical Coordinates 6.4 The Hydrogen Atom 7. Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function 7.1 The Matrix Formulation of Linear Operators 7.2 Dirac Notation 7.3 The Dirac Delta Function 8. Spin Angular Momentum 8.1 Spin Operators 8.2 Evidence for Spin 8.3 Adding Angular Momentum 8.4 The Matrix Representation of Spin 8.5 The Stern-Gerlach Experiment 8.6 Spin Precession 8.7 Spin Systems with Two Particles Noninteracting Spins Interacting Spins 8.8 Measurement Theory Hidden Variables The ManyWorlds Interpretation of Quantum Mechanics 9. Time-Independent Perturbation Theory 9.1 Derivation of Time-Independent Perturbation Theory 9.2 Perturbations to the Atomic Energy Levels Fine Structure The Lamb Shift 9.3 The Atom in External Electric or Magnetic Fields The Atom in an Electric Field: The Stark Effect The Atom in a Magnetic Field: The Zeeman Effect 10. The Variational Principle 10.1 Variational Principle: Theory 10.2 Variational Principle: Application to the Helium Atom 11. Time-Dependent Perturbation Theory 11.1 Derivation of Time-Dependent Perturbation Theory 11.2 Application: Selection Rules for Electromagnetic Radiation 12. Scattering Theory 12.1 Definition of the Cross Section 12.2 The Born Approximation 12.3 PartialWaves 13. The Multiparticle Schrodinger Equation 13.1 Wave Function for Identical Particles 13.2 Multielectron Atoms 14. Some Modern Applications of Quantum Mechanics 14.1 Magnetic Resonance Imaging 14.2 Quantum Computing 15. What Comes Next? Relativistic Quantum Mechanics 15.1 The Klein-Gordon Equation Derivation of the Klein-Gordon Equation Probability Densities and Currents 15.2 The Dirac Equation Answers and Hints for Selected End-of-Chapter Exercises Index

•Jan 1, 2006•18 citations

An Overview Of Quantum Electrodynamics And Matter–Radiation Field Interaction

Abraham Nitzan

Many dynamical processes of interest are either initiated or probed by light, and their understanding requires some knowledge of this subject. This chapter is included in order to make this text self contained by providing an overview of subjects that are used in various applications later in the text. In particular, it aims to supplement the elementary view of radiation–matter interaction as a time-dependent perturbation in the Hamiltonian, by describing some aspects of the quantum nature of the radiation field. This is done on two levels: The main body of this chapter is an essentially qualitative overview that ends with a treatment of spontaneous emission as an example. The Appendix gives some more details on the mathematical structure of the theory. In elementary treatments of the interaction of atoms and molecules with light, the radiation field is taken as a classical phenomenon.

Oxford University Press eBooks•Apr 6, 2006•0 citations
An overview of classical mechanics the transition to quantum mechanics classical treatment of electromagnetic fields and radiation quantum properties of the field time-dependent perturbation theory, transition probabilities and scattering the density operator and its role in quantum statistics first-order radiation processes second-order processes and the scattering of photons principles of nuclear magnetic resonance. (Part Contents).
An Overview of Classical Mechanics The Transition to Quantum Mechanics Classical Treatment of Electromagnetic Fields and Radiation Quantum Properties of the Field Time-Dependent Perturbation Theory, Transition Probabilities, and Scattering The Density Operator and Its Role in Quantum Statistics First-Order Radiation Processes Second-Order Processes and the Scattering of Photons Principles of Nuclear Magnetic Resonance Theory of Photon Counting Statistics Dynamic Structure Factors Linear Response Theory.
PART I: INTRODUCTION AND BACKGROUND 1. Introduction 2. Classical optics 3. Quantum mechanics 4. Radiative transitions in atoms PART II: PHOTONS 5. Photon statistics 6. Photon antibunching 7. Coherent states and squeezed light 8. Photon number states PART III: ATOM-PHOTON INTERACTIONS 9. Resonant light-atom interactions 10. Atoms in cavities 11. Cold atoms PART IV: QUANTUM INFORMATION PROCESSING 12. Quantum cryptography 13. Quantum computing 14. Entangled states and quantum teleportation APPENDICES A. Poisson statistics B. Parametric amplification C. The density of states D. Low dimensional semiconductor structures E. Nuclear magnetic resonance F. Bose-Einstein condensation
An Introduction to Advanced Quantum Physics presents important concepts from classical mechanics, electricity and magnetism, statistical physics, and quantum physics brought together to discuss the interaction of radiation and matter, selection rules, symmetries and conservation laws, scattering, relativistic quantum mechanics, apparent paradoxes, elementary quantum field theory, electromagnetic and weak interactions, and much more. This book consists of two parts:. Part 1 comprises the material suitable for a second course in quantum physics and covers::; Electromagnetic Radiation and Matter;
A Brief Survey of Analytical Dynamics, Discovery of Matrix Mechanics, Mathematical Preliminaries Postulates of Quantum Theory Equations of Motion, Hamiltonian Operator and the Commutation Relations Symmetries and Conservation Laws, Classical and Quantum Integrability Classical and Quantum Mechanical Degeneracies Bound State Energies for One-Dimensional Problems Exactly Solvable Potentials, Supersymmetry and Shape Invariance Supersymmetry and Superpotential Shape Invariant Potentials Two-Body Problem Determination of the Angular Momentum Eigenvalues Methods of Integration of the Heisenberg Equations of Motion Discrete-Time Formulation of the Heisenberg's Equations of Motion Quantum Tunneling Using Discrete-Time Formulation Integration of the Operator Differential Equations Perturbation Theory Other Methods of Approximation Heisenberg Correspondence Principle, Quantization of the Equations of Motion with Higher Derivatives Determinantal Method in Potential Scattering Time-Dependent Scattering Theory The Scattering Matrix Impact Parameter Representation of the Scattering Amplitude Transition Probability Quantum Diffraction, Motion of a Charged Particle in Electromagnetic Field The Aharanov-Bohm Effect Neutron Interferometry Quantum Many-Body Problem Hartree and Hartree-Fock Approximations Second Quantization Bogoliubov Transformation for a Many-Boson System Bogoliubov Transformation for Fermions Interacting Through Pairing Forces Quantum Theory of Free Electromagnetic Field Casimir Force Interaction of Radiation with Matter Heisenberg Equations for Interaction of an Atom with Radiation Bell's Inequalities
Table of Contents 1. The Origins of Quantum Mechanics 1.1 Introduction 1.2 Blackbody Radiation The Problem with Blackbody Radiation 1.3 The Nature of Light The Photoelectric Effect The Compton Effect Is it a Particle or a Wave? 1.4 TheWave Nature of Matter 1.5 The Bohr Atom 1.6 Where do we Stand? 2. Math Interlude A: Complex Numbers and Linear Operators 2.1 Complex Numbers 2.2 Operators Definition of an Operator Eigenfunctions and Eigenvalues 3. The Schrodinger Equation 3.1 Derivation of the Schrodinger Equation 3.2 The Meaning of theWave Function 3.3 The Time-Independent Schrodinger Equation Derivation of the Time-Independent Schrodinger Equation Qualitative Solutions and the Origin of Quantization 4. One-Dimensional Time-Independent Schrodinger Equation 4.1 Unbound States: Scattering and Tunneling Scattering From Step-Function Potentials 4.2 Bound Systems The Infinite SquareWell The Harmonic Oscillator Potential 5. Math Interlude B: Linear Algebra 5.1 Properties of Linear Operators 5.2 Vector Spaces Inner Products Adjoint and Hermitian Operators Basis Sets 6. The Three-Dimensional Time-Independent Schrodinger Equation 6.1 Solution in Rectangular Coordinates 6.2 Angular Momentum 6.3 The Schrodinger Equation in Spherical Coordinates 6.4 The Hydrogen Atom 7. Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function 7.1 The Matrix Formulation of Linear Operators 7.2 Dirac Notation 7.3 The Dirac Delta Function 8. Spin Angular Momentum 8.1 Spin Operators 8.2 Evidence for Spin 8.3 Adding Angular Momentum 8.4 The Matrix Representation of Spin 8.5 The Stern-Gerlach Experiment 8.6 Spin Precession 8.7 Spin Systems with Two Particles Noninteracting Spins Interacting Spins 8.8 Measurement Theory Hidden Variables The ManyWorlds Interpretation of Quantum Mechanics 9. Time-Independent Perturbation Theory 9.1 Derivation of Time-Independent Perturbation Theory 9.2 Perturbations to the Atomic Energy Levels Fine Structure The Lamb Shift 9.3 The Atom in External Electric or Magnetic Fields The Atom in an Electric Field: The Stark Effect The Atom in a Magnetic Field: The Zeeman Effect 10. The Variational Principle 10.1 Variational Principle: Theory 10.2 Variational Principle: Application to the Helium Atom 11. Time-Dependent Perturbation Theory 11.1 Derivation of Time-Dependent Perturbation Theory 11.2 Application: Selection Rules for Electromagnetic Radiation 12. Scattering Theory 12.1 Definition of the Cross Section 12.2 The Born Approximation 12.3 PartialWaves 13. The Multiparticle Schrodinger Equation 13.1 Wave Function for Identical Particles 13.2 Multielectron Atoms 14. Some Modern Applications of Quantum Mechanics 14.1 Magnetic Resonance Imaging 14.2 Quantum Computing 15. What Comes Next? Relativistic Quantum Mechanics 15.1 The Klein-Gordon Equation Derivation of the Klein-Gordon Equation Probability Densities and Currents 15.2 The Dirac Equation Answers and Hints for Selected End-of-Chapter Exercises Index
Many dynamical processes of interest are either initiated or probed by light, and their understanding requires some knowledge of this subject. This chapter is included in order to make this text self contained by providing an overview of subjects that are used in various applications later in the text. In particular, it aims to supplement the elementary view of radiation–matter interaction as a time-dependent perturbation in the Hamiltonian, by describing some aspects of the quantum nature of the radiation field. This is done on two levels: The main body of this chapter is an essentially qualitative overview that ends with a treatment of spontaneous emission as an example. The Appendix gives some more details on the mathematical structure of the theory. In elementary treatments of the interaction of atoms and molecules with light, the radiation field is taken as a classical phenomenon.