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Field Guide to Quantum Mechanics
Author(s): Brian P. Anderson
Published: 2019
https://doi.org/10.1117/3.2512268
PDF ISBN: 9781510622838 | Print ISBN: 9781510622821
TABLE OF CONTENTS
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Front Matter
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EBOOK TOPIC
Quantum States, Kets, and State Space
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Elements of Dirac Notation
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Vector Spaces and Scalar Products
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Linear Operators and Commutators
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Hermitian Conjugation
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Bases
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Eigenvalue Equations
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Projectors
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Closure Relations
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Functions of Operators
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Postulates of Quantum Mechanics
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Eigenvalue and Collapse Postulates
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Probability Postulate
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Examples of Observables: Hˆ , Xˆ , and Pˆx
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Calculating Quantities in Quantum Mechanics
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Calculating Quantities Using a Discrete Basis
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Discrete Representations
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Transformation of Discrete Representation
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Continuous Representations: Xˆ , Pˆx
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Continuous Representations: Wavefunctions
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Calculating Quantities Using a Continuous Basis
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Operators in the Xˆ Representation
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Xˆ and Pˆx Representations: Eigenkets and Operators
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Xˆ and Pˆx Representations: Fourier Transforms
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Tensor Products: Merging State Spaces
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Operator Definitions and Operator Manipulation
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Expectation Values
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Commutation Relations
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Non-Commuting Operators, Uncertainty Relations
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Complete Sets of Commuting Observables
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CSCOs for Specific Problems
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Properties of Wavefunctions
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Wave-Like Properties of Matter
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Graphical Interpretation of the Schrödinger Equation
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Graphical Interpretation: Example
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Superpositions, Relative and Global Phases
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Probability Currents
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Unitary Transformations
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Common Unitary Operators
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Conservative Systems
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Stationary States
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Time-Dependent Reference Frames
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Schrödinger, Heisenberg, and Interaction Pictures
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Schrödinger Picture: Expectation Value Dynamics
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Heisenberg Picture: Operators and Dynamics
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Interaction Picture
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Exactly Solvable Problems in One Dimension
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Free Particle and Delta Function Potential Well
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Infinite Square Well
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Potential Barrier: Transmission and Reflection
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Potential Barrier: Energy above Barrier
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Potential Barrier: Tunneling
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Potential Barrier: Examples
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1D Quantum Harmonic Oscillator
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Harmonic Oscillator: Energy Eigenfunctions
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Harmonic Oscillator: Ladder Operators
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Harmonic Oscillator: Properties and Dynamics
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Harmonic Oscillator: Fourier Transforms
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Coherent States (Quasi-Classical States)
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Phase-Space Diagrams
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Phase-Space Diagrams: Examples
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3D Quantum Harmonic Oscillator
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Angular Momentum: Definitions
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Angular Momentum: Eigenvalues and Eigenstates
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Orbital Angular Momentum: Operators
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Orbital Angular Momentum: Position Representation
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Spin Angular Momentum
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Spin Angular Momentum: s51/2
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Pauli Spin Operators
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Angular Momentum j = 1
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Magnetic Dipole Moments and Magnetic Fields
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Gyromagnetic Ratios and g-Factors
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Magnetic Moment Dynamics: Uniform Fields
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Magnetic Moment Dynamics: Gradient Fields
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Two-Level Systems
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Rabi Oscillations
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The Bloch Vector
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The Bloch Sphere
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Spin 1/2 in a Uniform Magnetic Field
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Spin 1/2 in a Uniform Magnetic Field: Dynamics
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Bloch Vector Dynamics: Examples
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Addition of Two Angular Momenta
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Total Angular Momentum Basis
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Addition of Angular Momentum: Example
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Addition of Angular Momentum: Comments
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Clebsch–Gordan Coefficients
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Clebsch–Gordan Coefficients: Usage
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Clebsch–Gordan Coefficients: Examples
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Ritz Variational Method
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Stationary Perturbation Theory
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Degenerate Stationary Perturbation Theory
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Time-Dependent Perturbation Theory
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TDPT: First-Order Solution
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Fourier Transform Pairs for Pulse Perturbations
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TDPT: Harmonic Perturbations
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Central Potential Problems
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“Spinless” Hydrogen: Energy Eigenvalues
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Spinless Hydrogen: Energy Eigenfunctions
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Hydrogen Radial Wavefunctions
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Spherical Harmonics
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Atomic Angular Momentum Quantum Numbers
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Fine Structure of Hydrogen: Perturbation Terms
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Fine Structure of Hydrogen: Solutions
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Hyperfine Structure of Hydrogen
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Zeeman Effect in Hydrogen: n51
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Zeeman Effect in Hydrogen: n51 Solutions
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Spectroscopic Notation and Term Symbols
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Identical Particles: Two Particles
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Identical Particles: Three or More Particles
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Identical Particles: Occupation Number Basis
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Identical Particles: Occupation Number Basis States
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Miscellaneous Symbols and Notation
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Linear Algebra Basics
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Eigenvalue Equations in Linear Algebra
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Spherical Coordinates
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Operators in Spherical Coordinates
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Properties of 1D Gaussian Wavefunctions
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Clebsch–Gordan Coefficient Tables: J1×1/2
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Clebsch–Gordan Coefficient Tables: J1×1
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Clebsch–Gordan Coefficient Tables: J1×3/2
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Clebsch–Gordan Coefficient Tables: 2×2
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Integrals of Exponential Forms
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Identities and Series Expansions
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Dimensional Units (SI)
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Common Physical Constants (to Four Significant Digits)
EBOOK TOPIC Open Access
Back Matter
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