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Holzner S. Quantum Physics For Dummies

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Holzner S. Quantum Physics For Dummies
Rev. ed. — John Wiley & Sons, Inc. 2013. — 338 p.
Quantum Physics For Dummies, Revised Edition helps make quantum physics understandable and accessible. From what quantum physics can do for the world to understanding hydrogen atoms, readers will get complete coverage of the subject, along with numerous examples to help them tackle the tough equations. Compatible with classroom text books and courses, Quantum Physics For Dummies, Revised Edition lets students study at their own paces and helps them prepare for graduate or professional exams. Coverage includes:
The Schrodinger Equation and its Applications
The Foundations of Quantum Physics
Vector Notation
Spin
Scattering Theory, Angular Momentum, and more
Your plain-English guide to understanding and working with the micro world
Quantum physics — also called quantum mechanics or quantum field theory — can be daunting for even the most dedicated student or enthusiast of science, math, or physics. This friendly, concise guide makes this challenging subject understandable and accessible, from atoms to particles to gases and beyond. Plus, it's packed with fully explained examples to help you tackle the tricky equations like a pro!
Compatible with any classroom course — study at your own pace and prepare for graduate or professional exams
Your journey begins here — understand what quantum physics is and what kinds of problems it can solve
Know the basic math — from state vectors to quantum matrix manipulations, get the foundation you need to proceed
Put quantum physics to work — make sense of Schrödinger's equation and handle particles bound in square wells and harmonic oscillators
Solve problems in three dimensions — use the full operators to handle wave functions and eigenvectors to find the natural wave functions of a system
Discover the latest research — learn the cutting-edge quantum physics theories that aim to explain the universe itself
About the Author
Introduction
About This Book
Conventions Used in This Book
Foolish Assumptions
How This Book Is Organized
Part I: Small World, Huh? Essential Quantum Physics
Part II: Bound and Undetermined: Handling Particles in Bound States
Part III: Turning to Angular Momentum and Spin
Part IV: Multiple Dimensions: Going 3D with Quantum Physics
Part V: Group Dynamics: Introducing Multiple Particles
Part VI: The Part of Tens
Icons Used in This Book
Where to Go from Here
Small World, Huh? Essential Quantum Physics
Discoveries and Essential Quantum Physics
Being Discrete: The Trouble with Black-Body Radiation
First attempt: Wien's Formula
Second attempt: Rayleigh-Jeans Law
An intuitive (quantum) leap: Max Planck's spectrum
The First Pieces: Seeing Light as Particles
Solving the photoelectric effect
Scattering light off electrons: The Compton effect
Proof positron? Dirac and pair production
A Dual Identity: Looking at Particles as Waves
You Can't Know Everything (But You Can Figure the Odds)
The Heisenberg uncertainty principle
Rolling the dice: Quantum physics and probability
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 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
Preparing for the Inversion: Simplifying with Unitary Operators
Comparing Matrix and Continuous Representations
Going continuous with calculus
Doing the wave
Bound and Undetermined: Handling Particles in Bound States
Getting Stuck in Energy Wells
Looking into a Square Well
Trapping Particles in Potential Wells
Binding particles in potential wells
Escaping from potential wells
Trapping Particles in Infinite Square Potential Wells
Finding a 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
Assuming the particle doesn't have enough energy
Hitting the Wall: Particles and Potential Barriers
Getting through potential barriers when E> V0
Getting through potential barriers, even 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
Back and Forth with Harmonic Oscillators
Grappling with the Harmonic Oscillator Hamiltonians
Going classical with harmonic oscillation
Understanding total energy in quantum oscillation
Creation and Annihilation: Introducing the Harmonic Oscillator Operators
Mind your p's and q's: Getting the energy state equations
Finding the Eigenstates
Using a and a† directly
Finding the harmonic oscillator energy eigenstates
Putting in some numbers
Looking at Harmonic Oscillator Operators as Matrices
A Jolt of Java: Using Code to Solve the Schrödinger Equation Numerically
Making your approximations
Building the actual code
Running the code
Turning to Angular Momentum and Spin
Working with Angular Momentum on the Quantum Level
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
Getting rotational energy of a diatomic molecule
Finding the Eigenvalues of the Raising and Lowering Operators
Interpreting Angular Momentum with Matrices
Rounding It Out: Switching to the Spherical Coordinate System
The eigenfunctions of Lz in spherical coordinates
The eigenfunctions of L2 in spherical coordinates
Getting Dizzy with Spin
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
Working with Spin ½ and Pauli Matrices
Spin ½ matrices
Pauli matrices
[iMultiple Dimensions: Going 3D with Quantum Physics[/i]
Rectangular Coordinates: Solving Problems in Three Dimensions
The Schrödinger Equation: Now in 3D!
Solving Three-Dimensional Free Particle Problems
The x, y, and z equations
Finding the total energy equation
Adding time dependence and getting a physical solution
Getting Squared Away with 3D Rectangular Potentials
Determining the energy levels
Normalizing the wave function
Using a cubic potential
Springing into 3D Harmonic Oscillators
Solving Problems in Three Dimensions: Spherical Coordinates
A New Angle: Choosing Spherical Coordinates Instead of Rectangular
Taking a Good Look at 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
Inside the square well: 0 < r < a
Outside the square well: r > a
Getting the Goods on Isotropic Harmonic Oscillators
Understanding Hydrogen Atoms
Coming to Terms: The Schrödinger Equation for the Hydrogen Atom
Simplifying and Splitting the Schrödinger Equation for Hydrogen
Solving for ψ(R)
Solving for ψ(r)
Solving the radial Schrödinger equation for small r
Solving the radial Schrödinger equation for large r
You got the power: Putting together the solution for the radial equation
Fixing f(r) to keep it finite
Finding the allowed energies of the hydrogen atom
Getting the form of the radial solution of the Schrödinger equation
Some hydrogen wave functions
Calculating the Energy Degeneracy of the Hydrogen Atom
Quantum states: Adding a little spin
On the lines: Getting the orbitals
Hunting the Elusive Electron
Handling Many Identical Particles
Many-Particle Systems, Generally Speaking
Considering wave functions and Hamiltonians
A Nobel opportunity: Considering multi-electron atoms
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
Name that composite: Grooving with the symmetrization postulate
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
Group Dynamics: Introducing Multiple Particles
Giving Systems a Push: Perturbation Theory
Introducing Time-Independent Perturbation Theory
Working with Perturbations to Nondegenerate Hamiltonians
A little expansion: Perturbing the equations
Matching the coefficients of λ and simplifying
Finding the first-order corrections
Finding the second-order corrections
Perturbation Theory to the Test: Harmonic Oscillators in Electric Fields
Finding exact solutions
Applying perturbation theory
Working with Perturbations to Degenerate Hamiltonians
Testing Degenerate Perturbation Theory: Hydrogen in Electric Fields
Wham-Blam! Scattering Theory
Introducing Particle Scattering and Cross Sections
Translating between the Center-of-Mass and Lab Frames
Framing the scattering discussion
Relating the scattering angles between frames
Translating cross sections between the frames
Trying a lab-frame example with particles of equal mass
Tracking the Scattering Amplitude of Spinless Particles
The incident wave function
The scattered wave function
Relating the scattering amplitude and differential cross section
Finding the scattering amplitude
The Born Approximation: Rescuing the Wave Equation
Exploring the far limits of the wave function
Using the first Born approximation
Putting the Born approximation to work
The Part of Tens
Ten Quantum Physics Tutorials
An Introduction to Quantum Mechanics
Quantum Mechanics Tutorial
Grains of Mystique: Quantum Physics for the Layman
Quantum Physics Online Version 2.0
Todd K. Timberlake's Tutorial
Physics 24/7's Tutorial
Stan Zochowski's PDF Tutorials
Quantum Atom Tutorial
College of St. Benedict's Tutorial
A Web-Based Quantum Mechanics Course
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
Glossary
Index
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