About this title: Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples is a comprehensive introduction to non-relativistic quantum mechanics for advanced undergraduate students in physics and related fields. It provides students with a strong conceptual background in the most important
theoretical aspects of quantum mechanics, extensive experience with the mathematical tools required to solve problems, the opportunity to use quantum ideas to confront modern experimental realizations of quantum systems, and numerous visualizations of quantum concepts and phenomena. Changes from the
First Edition include many new discussions of modern quantum systems (such as Bose-Einstein condensates, the quantum Hall effect, and wave packet revivals) all in the context of familiar textbook level examples. The book continues to emphasize the many connections to classical mechanics and wave
physics to help students use their existing intuition to better learn new quantum concepts.
Table Of Contents
Part I The Quantum Paradigm
A First Look at Quantum Physics
How this Book Approaches Quantum Mechanics
Essential Relativity
Quantum Physics: h as a Fundamental Constant
Semiclassical Model of the Hydrogen Atom
Dimensional Analysis
Questions and Problems
Classical Waves
The Classical Wave Equation
Wave Packets and Periodic Solutions
General Wave Packet Solutions
Fourier Series
Fourier Transforms
Inverting the Fourier transform: the Dirac δ-function
Dispersion and Tunneling
Velocities for Wave Packets
Dispersion
Tunneling
Questions and Problems
The Schrodinger Wave Equation
The Schrodinger Equation
Plane Waves and Wave Packet Solutions
Plane Waves and Wave Packets
The Gaussian Wave Packet
``Bouncing'' Wave Packets
Numerical Calculation of Wave Packets
Questions and Problems
Interpreting the Schrodinger Equation
Introduction to Probability
Discrete Probability Distributions
Continuous Probability Distributions
Probability Interpretation of the Schrodinger Wavefunction
Average Values
Average Values of Position
Average Values of Momentum
Average Values of Other Operators
Real Average Values and Hermitian Operators
The Physical Interpretation of Φ (p)
Energy Eigenstates, Stationary States, and the Hamiltonian Operator
The Schrodinger Equation in Momentum Space
Transforming the Schrodinger Equation Into Momentum Space
Uniformly Accelerating Particle
Commutators
The Wigner Quasi-Probability Distribution
Questions and Problems
The Infinite Well: Physical Aspects
The Infinite Well in Classical Mechanics: Classical Probability Distributions
Stationary States for the Infinite Well
Position-Space Wavefunctions for the Standard Infinite Well
Expectation Values and Momentum-Space Wavefunctions for the Standard Infinite Well
The Symmetric Infinite Well
The Asymmetric Infinite Well
Time-Dependence of General Solutions
Two-State Systems
Wave Packets in the Infinite Well
Wave Packets Versus Stationary States
Questions and Problems
The Infinite Well: Formal Aspects
Dirac Bracket Notation
Eigenvalues of Hermitian Operators
Orthogonality of Energy Eigenfunctions
Expansions in Eigenstates
Expansion Postulate and Time-Dependence
Parity
Simultaneous Eigenfunctions
Questions and Problems
Many Particles in the Infinite Well: The Role of Spin and Indistinguishability
The Exclusion Principle
One-Dimensional Systems
Three-Dimensional Infinite Well
Applications
Conduction Electrons in a Metal
Neutrons and Protons in Atomic Nuclei
White Dwarf and Neutron Stars
Questions and Problems
Other One-Dimensional Potentials
Singular Potentials
Continuity of ψ (x)
Single δ-function Potential
Twin δ-function Potential
Infinite Array of δ-functions: Periodic Potentials and the Dirac Comb
The Finite Well
Formal Solutions
Physical Implications and the Large x Behavior of Wavefunctions
Applications to Three-Dimensional Problems
The Schrodinger Equation in Three Dimensions
Model of the Deuteron
Questions and Problems
The Harmonic Oscillator
The Importance of the Simple Harmonic Oscillator
Solutions for the SHO
Differential Equation Approach
Properties of the Solutions
Experimental Realizations of the SHO
Classical Limits and Probability Distributions
Unstable Equilibrium: Classical and Quantum Distributions
Questions and Problems
Alternative Methods of Solution and Approximation Methods
Numerical Integration
The Variational or Rayleigh-Ritz Method
The WKB method
WKB Wavefunctions
WKB Quantized Energy Levels
Matrix Methods
Perturbation Theory
Nondegenerate States
Degenerate Perturbation Theory
Time-Dependent Perturbation Theory
Questions and Problems
Scattering
Scattering in One-Dimensional Systems
Bound and Unbound States
Plane Wave Solutions
Scattering from a Step Potential
Scattering from the Finite Square Well
Attractive Well
Repulsive Barrier
Applications of Quantum Tunneling
Field Emission
Scanning Tunneling Microscopy
α-Particle Decay of Nuclei
Nuclear Fusion Reactions
Questions and Problems
More Formal Topics
Hermitian Operators
Quantum Mechanics, Linear Algebra, and Vector Spaces
Commutators
Uncertainty Principles
Time-Dependence and Conservation Laws in Quantum Mechanics
Propagators
General Case and Free Particles
Propagator and Wave Packets for the Harmonic Oscillator
Timescales in Bound State Systems: Classical Period and Quantum Revival Times
Questions and Problems
Operator and Factorization Methods for the Schrodinger Equation
Factorization Methods
Factorization of the Harmonic Oscillator
Creation and Annihilation Operators
Questions and Problems
Multiparticle Systems
Generalities
Separable Systems
Two-Body Systems
Classical Systems
Quantum Case
Spin Wavefunctions
Indistinguishable Particles
Questions and Problems
Part II The Quantum World
Two-Dimensional Quantum Mechanics
2D Cartesian Systems
2D Infinite Well
2D Harmonic Oscillator
Central Forces and Angular Momentum
Classical Case
Quantum Angular Momentum in 2D
Quantum Systems with Circular Symmetry
Free Particle
Circular Infinite Well
Isotropic Harmonic Oscillator
Questions and Problems
The Schrodinger Equation in Three Dimensions
Spherical Coordinates and Angular Momentum
Eigenfunctions of Angular Momentum
Methods of Derivation
Visualization and Applications
Classical Limit of Rotational Motion
Diatomic Molecules
Rigid Rotators
Molecular Energy Levels
Selection Rules
Spin and Angular Momentum
Addition of Angular Momentum
Free Particle in Spherical Coordinates
Questions and Problems
The Hydrogen Atom
Hydrogen Atom Wavefunctions and Energies
The Classical Limit of the Quantum Kepler Problem
Other ``Hydrogenic'' Atoms
Rydberg Atoms
Muonic Atoms
Multielectron Atoms
Helium-Like Atoms
Lithium-Like Atoms
The Periodic Table
Questions and Problems
Gravity and Electromagnetism in Quantum Mechanics
Classical Gravity and Quantum Mechanics
Electromagnetic Fields
Classical Electric and Magnetic Fields
E and B Fields in Quantum Mechanics
Constant Electric Fields
Atoms in Electric Fields: The Stark Effect
Classical Case
Quantum Stark Effect
Constant Magnetic Fields
Atoms in Magnetic Fields
The Zeeman Effect External B Fields
Spin-Orbit Splittings: Internal B Fields
Hyperfine Splittings: Magnetic Dipole-Dipole Interactions
Spins in Magnetic Fields
Measuring the Spinor Nature of the Neutron Wavefunction
Spin Resonance
The Aharonov-Bohm Effect
Questions and Problems
Scattering in Three Dimensions
Classical Trajectories and Cross-Sections
Quantum Scattering
Cross-Section and Flux
Wave Equation for Scattering and the Born Approximation
Electromagnetic Scattering
Partial Wave Expansions
Scattering of Particles
Frames of Reference
Identical Particle Effects
Questions and Problems
A. Dimensions and MKS-type Units for Mechanics, Electricity and Magnetism, and Thermal Physics
Problems
B. Physical Constants, Gaussian Integrals, and the Greek Alphabet
Physical Constants
The Greek Alphabet
Gaussian Probability Distribution
Problems
C. Complex Numbers and Functions
Problems
D. Integrals, Summations, and Calculus Results
Integrals
Summations and Series Expansions
Assorted Calculus Results
Real Integrals by Contour Integration
Plotting
Problems
E. Special Functions
Trigonometric and Exponential Functions
Airy Functions
Hermite Polynomials
Cylindrical Bessel Functions
Spherical Bessel Functions
Legendre Polynomials
Generalized Laguerre Polynomials
The Dirac δ-Function
The Euler Gamma Function
Problems
F. Vectors, Matrices, and Group Theory
Vectors and Matrices
Group Theory
Problems
G. Hamiltonian Formulation of Classical Mechanics
Problems
References
Index
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