Quantum Physics for Dummies, 3rd Edition

Title Page
Copyright Page
Table of Contents
Introduction
	About This Book
	Foolish Assumptions
	Icons Used in This Book
	Beyond the Book
	Where to Go from Here
Part 1 Getting Started with Quantum Physics
	Chapter 1 What Is Quantum Physics, Anyway?
		The Classics: Pre-Quantum Physics
		What Makes Physics Quantum?
		A Matter of Scale, or a Scale of Matter
		Measurements and Observables: How Scientists Know Quantum Physics Is True
			Doing the right tests
			Trusting (but verifying) the right tests
	Chapter 2 Standing on the Shoulders of Giants: Classical Physics
		Objects in Motion: Classical Mechanics
			Newton makes the rules
				Describing motion
				Applying calculus to the motion
			Kinetic energy and momentum
				Finding momentum when direction matters
				Focusing on kinetic energy — but others exist
		Catching the Waves
			Some wavefront properties
			Wave interference and superposition
		Let There Be Light: Electromagnetism
			A light dispute: Corpuscles versus vibrations
				Dealing with obstructions
				Theories to explain light’s behavior
			Young’s double slit contradiction
			Maxwell’s marvelous equations
				Connecting the forces
				Expressing the connections with math
			Michelson-Morley and the mysterious missing ether
				Looking for the ether
				Comparing the light on two paths
		Atoms: Building Blocks of Matter
			Ancient atomism
			Chemists discover the atom (maybe)
			And the electron
		Thermodynamics: Another Hot Topic
		The Games People Play: Unknowns and Uncertainties
			A roll of the dice: Classical probability
				Figuring the probability of an outcome for one die
				Letting probabilities simplify your analyses
			Uncertainties and deviations
				Accounting for measurement uncertainties
				Putting statistical notions to use
	Chapter 3 The Quantum Revolution
		Being Discrete: The Trouble with Black-Body Radiation
			An intuitive (quantum) leap: Max Planck’s spectrum
		Seeing Light as Particles
			Solving the photoelectric effect
			Scattering light off electrons: The Compton effect
		Bohr’s Atomic Model
			The changing of electron orbits
			Explaining results by using Bohr’s model
		A Dual Identity: Looking at Particles as Waves
		Proof Positron? Dirac and Pair Production
		You Can’t Know Everything (But You Can Figure the Odds)
			Position versus momentum: The Heisenberg uncertainty principle
				Understanding uncertainty when taking measurements
				Quantifying uncertainty
				Applying uncertainty to particle physics
			Rolling quantum dice: A new take on probability
				Two approaches to outcome probabilities
				Exploiting a wave function
		A New Take on Light: Quantum Electrodynamics
			What is doing the waving?
			First glimmers of QED
			The photon gets a new job
				Visualizing with Feynman’s diagrams
				Tying Feynman’s diagrams to quantum electrodynamics
		Breaking Open the Atom’s Bits
			Banging particles together to get information out
			Holding the atomic nucleus together
Part 2 The Fundamentals: Quantum Physics Principles and Theories
	Chapter 4 Quantum Mechanics: Particle States and Dualities
		Quantifying by Quantum Numbers
			The ever-spinning electron
			Fermions and bosons
		Revisiting Wave-Particle Duality
			Origins of wave-particle duality
			Implications of wave-particle duality
		Discovering What Antimatter Is
	Chapter 5 Quantum Electrodynamics and Beyond
		Quantum Field Theory: Explaining Matter and Energy
			Revisiting quantum electrodynamics
			Looking at nuclear forces and quantum chromodynamics
			Calling on the Higgs boson
		Discovering How Quantum Physics Changed the World
			Letting there be light with lasers
			Controlling the flow with semiconductors and transistors
			Harnessing the power of nuclear energy
				Energy through nuclear fission
				Energy through nuclear fusion
			Going solar
		Looking Ahead at Quantum Computers
			Calculating with superposition states
			Sustaining and evolving quantum computers
	Chapter 6 Quantum Cats and Spooky Action: Interpretations of Quantum Physics
		Questioning What Needs Interpretation
			Interpreting probability and measurement
			Interpreting the observer effect
			Entanglement revisited
		Discovering That the Most Common Interpretation Is to Shrug
		Outlining Three Quantum Physics Interpretations
			The popular one: Copenhagen interpretation
			The fun one: Many worlds interpretation
			The responsible one: Hidden variables
		Enduring Debates, Bickering, and Other Counterarguments
			Addressing the (dead?) cat in the room
			Getting spooked with Einstein
				Setting assumptions and relating theories
				Looking for a complete interpretation
		Exploring Entangled Experiments
			Bell’s inequality
			Alain Aspect’s grand experiment
Part 3 By the Numbers: Basic Quantum Physics Math
	Chapter 7 Entering the Matrix: Welcome to State Vectors
		Creating Your Own Vectors in Hilbert Space
		Making Life Easier with Dirac Notation
			Abbreviating state vectors as kets
			Writing the Hermitian conjugate as a bra
			Multiplying bras and kets: A probability of 1
			Covering all your bases: Bras and kets as basis-less state vectors
			Understanding some relationships by using kets
		Grooving with Operators
			Hello, operator: How operators work
			I expected that: Finding expectation values
			Looking at linear operators
			Going Hermitian with Hermitian operators and adjoints
		Forward and Backward: Finding the Commutator
			Commuting
			Finding anti-Hermitian operators
		Starting from Scratch and Ending Up with Heisenberg
		Eigenvectors and Eigenvalues: They’re Naturally Eigentastic!
			Understanding how they work
			Finding eigenvectors and eigenvalues
				Finding eigenvalues
				Finding eigenvectors
		Preparing for the Inversion: Simplifying with Unitary Operators
		Comparing Matrix and Continuous Representations
			Going continuous with calculus
			Doing the wave
	Chapter 8 Getting Stuck in Energy Wells
		Looking into a Square Well
		Trapping Particles in Potential Wells
			Binding particles in potential wells
			Escaping from potential wells
				Case 1: Energy between the two potentials (V1 < E < V2)
				Case 2: Energy greater than the higher potential (E > V2)
		Trapping Particles in Infinite Square Potential Wells
			Finding the wave function equation
			Determining the energy levels
			Normalizing the wave function
			Adding time dependence to wave functions
			Shifting to symmetric square well potentials
		Limited Potential: Taking a Look at Particles and Potential Steps
			Assuming the particle has plenty of energy
				Calculating the probability of reflection or transmission
				Those pesky constants: Finding A, B, and C
			Assuming the particle doesn’t have enough energy
				Finding transmission and reflection coefficients
				The nonzero solution: Finding a particle in x > 0
		Tunneling through Forbidden Regions
		Hitting the Wall: Particles and Potential Barriers
			Getting through potential barriers when E > V0
			Tunneling through: Potential barriers when E < V0
		Particles Unbound: Solving the Schrödinger Equation for Free Particles
			Getting a physical particle with a wave packet
			Going through a Gaussian example
	Chapter 9 Back and Forth with Harmonic Oscillators
		Grappling with the Harmonic Oscillator Hamiltonians
			Going classical with harmonic oscillation
			Understanding total energy in quantum oscillation
				Putting the Hamiltonian to use
				Applying the Hamiltonian to eigenstates
		Creation and Annihilation: Introducing the Harmonic Oscillator Operators
		Mind Your p’s and q’s: Getting the Energy State Equations
		Finding the Eigenstates
			Finding the energy of a|n
			Finding the energy of a†|n
			Deriving a and a† directly
			Finding the harmonic oscillator energy eigenstates
				Working in position space
				A little excitement: Finding the first excited state
				Finding the second excited state
				Using hermite polynomials to find any excited state
			Reality check: Putting in some numbers
	Chapter 10 Working with Angular Momentum on the Quantum Level
		Setting Up the Hamiltonian
		Ringing the Operators: Round and Round with Angular Momentum
		Finding Commutators of Lx, Ly, and Lz
		Creating the Angular Momentum Eigenstates
		Finding the Angular Momentum Eigenvalues
			Deriving eigenstate equations with βmax and βmin
				Further investigating the quantum numbers
				Looking at the results intuitively
			Getting the rotational energy of a diatomic molecule
		Finding the Eigenvalues of the Raising and Lowering Operators
		Interpreting Angular Momentum with Matrices
			Raising and lowering operators
			Moving on to other L operators
		Rounding It Out: Switching to the Spherical Coordinate System
			Laying the (spherical) groundwork
			The eigenfunctions of Lz in spherical coordinates
			The eigenfunctions of L2 in spherical coordinates
			Moving back to rectangular coordinates
	Chapter 11 Getting Dizzy with Spin
		Investigating the Stern-Gerlach Experiment and the Case of the Missing Spot
		Getting Down and Dirty with Spin and Eigenstates
		Halves and Integers: Saying Hello to Fermions and Bosons
		Spin Operators: Running Around with Angular Momentum
			Defining the spin operators
			Raising and lowering spin operators
		Working with Spin ½ and Pauli Matrices
			Spin ½ matrices
				Spin up and spin down eigenstates
				The matrix operator S2
				The matrix operator Sz
				Raising and lowering spin with matrices
			Pauli matrices
Part 4 Going 3D with Quantum Physics Calculations
	Chapter 12 Rectangular Coordinates: Solving Problems in 3D
		Viewing the Schrödinger Equation in 3D!
			Converting the Schrödinger equation into rectangular coordinates
			Separating the Schrödinger equation
		Solving 3D Free Particle Problems
			Finding the total energy equation
			Adding time dependence
			Finding a physical solution
		Getting Squared Away with 3D Rectangular Potentials
			Determining the energy levels
			Normalizing the wave function
			Using a cubic potential
				Degenerate energies and symmetry
				Cubic potential wave function
		Springing into 3D Harmonic Oscillators
			Potential of a 3D spring
			Solving Schrödinger for the 3D spring
			Energy of the 3D oscillator
	Chapter 13 Solving Spherical Coordinate Problems
		Choosing Spherical Coordinates
		Observing Central Potentials in 3D
			Breaking down the Schrödinger equation
			The angular part of ψ(r, θ, ϕ)
			The radial part of ψ(r, θ, ϕ)
		Handling Free Particles in 3D with Spherical Coordinates
			The spherical Bessel and Neumann functions
			The limits for small and large ρ
		Handling the Spherical Square Well Potential
			Looking inside the square well: 0 < r < a
			Outside the square well: r > a
		Getting the Goods on Isotropic Harmonic Oscillators
	Chapter 14 The Simplest Atom: Understanding Hydrogen
		Revisiting Atomism
		Coming to Terms: The Schrödinger Equation for the Hydrogen Atom
			Simplifying and splitting the hydrogen equation
			Solving the radial Schrödinger equation
				Looking at small r
				Looking at large r
				Looking at both r solutions
				Powering through the differential equation
				Fixing f(r) to keep it finite
			Finding the allowed energies of the hydrogen atom
			Crafting the form of the radial solution
		Going General with the Hydrogen Wave Function
		Calculating the Energy Degeneracy of the Hydrogen Atom
			Quantum states: Adding a little spin
				Wave functions for spin states
				Spin’s effect on degeneracy
			On the lines: Getting the orbitals
		Hunting the Elusive Electron
	Chapter 15 Handling Many Particles and Group Dynamics
		Many-Particle Systems, Generally Speaking
			Considering wave functions and Hamiltonians
			A Nobel opportunity: Considering multi-electron atoms
			Looking at a super-powerful tool: Interchange symmetry
				Order matters: Swapping particles with the exchange operator
				Classifying symmetric and antisymmetric wave functions
			Floating cars: Tackling systems of many distinguishable particles
			Juggling many identical particles
				Losing identity
				Symmetry and antisymmetry
				Exchange degeneracy: The steady Hamiltonian
			Building symmetric and antisymmetric wave functions
		Working with Identical Noninteracting Particles
			Wave functions of two-particle systems
			Wave functions of three-or-more-particle systems
			It’s not come one, come all: The Pauli exclusion principle
			Figuring out the periodic table
				Noting the electron shell structure
				Filling up the electron shells
		Giving Systems a Push: Perturbation Theory
			Introducing perturbation theory
			Working with perturbations to nondegenerate Hamiltonians
				Perturbation theory to the test: Harmonic oscillators in electric fields
				Wave functions of the charged oscillator
			Working with perturbations to degenerate Hamiltonians
		When Particles Collide: Scattering Theory
			Introducing particle scattering and cross sections
			Translating between the center-of-mass and lab frames
			Tracking the scattering amplitude of spinless particles
				Starting with the effective particle-of-mass equation
				Continuing with the scattered wave function
			The Born approximation: Rescuing the wave equation
Part 5 The Part of Tens
	Chapter 16 Ten Important Quantum Physics Pioneers
		Max Planck (1858–1947)
		Albert Einstein (1879–1955)
		Niels Bohr (1885–1962)
		Louis de Broglie (1892–1987)
		Werner Heisenberg (1901–1976)
		Erwin Schrödinger (1887–1961)
		Paul Dirac (1902–1984)
		Max Born (1882–1970)
		Richard Feynman (1918–1988)
		Murray Gell-Mann (1929–2019)
	Chapter 17 Ten Quantum Physics Triumphs
		Wave-Particle Duality
		The Photoelectric Effect
		Postulating Spin
		Differences between Newton’s Laws and Quantum Physics
		Heisenberg Uncertainty Principle
		Quantum Tunneling
		Discrete Spectra of Atoms
		Harmonic Oscillator
		Square Wells
		Schrödinger’s Cat
Index
EULA