Quantum Physics For Dummies, Revised Edition

Quantum Physics For Dummies, Revised Edition

by Steven Holzner
Released January 2013
Publisher(s): For Dummies
ISBN: 9781118460887

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Book description

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

    •

    Table of contents

    1. Cover Page
    2. Title Page
    3. Copyright
    4. About the Author
    5. Author's Acknowledgments
    6. Publisher's Acknowledgments
    7. Contents at a Glance
    8. Contents
    9. Introduction
      1. About This Book
      2. Conventions Used in This Book
      3. Foolish Assumptions
      4. How This Book Is Organized
        1. Part I: Small World, Huh? Essential Quantum Physics
        2. Part II: Bound and Undetermined: Handling Particles in Bound States
        3. Part III: Turning to Angular Momentum and Spin
        4. Part IV: Multiple Dimensions: Going 3D with Quantum Physics
        5. Part V: Group Dynamics: Introducing Multiple Particles
        6. Part VI: The Part of Tens
      5. Icons Used in This Book
      6. Where to Go from Here
    10. Part I: Small World, Huh? Essential Quantum Physics
      1. Chapter 1: Discoveries and Essential Quantum Physics
        1. Being Discrete: The Trouble with Black-Body Radiation
          1. First attempt: Wien's Formula
          2. Second attempt: Rayleigh-Jeans Law
          3. An intuitive (quantum) leap: Max Planck's spectrum
        2. The First Pieces: Seeing Light as Particles
          1. Solving the photoelectric effect
          2. Scattering light off electrons: The Compton effect
          3. Proof positron? Dirac and pair production
        3. A Dual Identity: Looking at Particles as Waves
        4. You Can't Know Everything (But You Can Figure the Odds)
          1. The Heisenberg uncertainty principle
          2. Rolling the dice: Quantum physics and probability
      2. Chapter 2: Entering the Matrix: Welcome to State Vectors
        1. Creating Your Own Vectors in Hilbert Space
        2. Making Life Easier with Dirac Notation
          1. Abbreviating state vectors as kets
          2. Writing the Hermitian conjugate as a bra
          3. Multiplying bras and kets: A probability of 1
          4. Covering all your bases: Bras and kets as basis-less state vectors
          5. Understanding some relationships using kets
        3. Grooving with Operators
          1. Hello, operator: How operators work
          2. I expected that: Finding expectation values
          3. Looking at linear operators
        4. Going Hermitian with Hermitian Operators and Adjoints
        5. Forward and Backward: Finding the Commutator
          1. Commuting
          2. Finding anti-Hermitian operators
        6. Starting from Scratch and Ending Up with Heisenberg
        7. Eigenvectors and Eigenvalues: They're Naturally Eigentastic!
          1. Understanding how they work
          2. Finding eigenvectors and eigenvalues
        8. Preparing for the Inversion: Simplifying with Unitary Operators
        9. Comparing Matrix and Continuous Representations
          1. Going continuous with calculus
          2. Doing the wave
    11. Part II: Bound and Undetermined: Handling Particles in Bound States
      1. Chapter 3: Getting Stuck in Energy Wells
        1. Looking into a Square Well
        2. Trapping Particles in Potential Wells
          1. Binding particles in potential wells
          2. Escaping from potential wells
        3. Trapping Particles in Infinite Square Potential Wells
          1. Finding a wave-function equation
          2. Determining the energy levels
          3. Normalizing the wave function
          4. Adding time dependence to wave functions
          5. Shifting to symmetric square well potentials
        4. Limited Potential: Taking a Look at Particles and Potential Steps
          1. Assuming the particle has plenty of energy
          2. Assuming the particle doesn't have enough energy
        5. Hitting the Wall: Particles and Potential Barriers
          1. Getting through potential barriers when E > V0
          2. Getting through potential barriers, even when E < V0
        6. Particles Unbound: Solving the Schrödinger Equation for Free Particles
          1. Getting a physical particle with a wave packet
          2. Going through a Gaussian example
      2. Chapter 4: Back and Forth with Harmonic Oscillators
        1. Grappling with the Harmonic Oscillator Hamiltonians
          1. Going classical with harmonic oscillation
          2. Understanding total energy in quantum oscillation
        2. Creation and Annihilation: Introducing the Harmonic Oscillator Operators
          1. Mind your p's and q's: Getting the energy state equations
        3. Finding the Eigenstates
          1. Using a and a† directly
          2. Finding the harmonic oscillator energy eigenstates
          3. Putting in some numbers
        4. Looking at Harmonic Oscillator Operators as Matrices
        5. A Jolt of Java: Using Code to Solve the Schrödinger Equation Numerically
          1. Making your approximations
          2. Building the actual code
          3. Running the code
    12. Part III: Turning to Angular Momentum and Spin
      1. Chapter 5: Working with Angular Momentum on the Quantum Level
        1. Ringing the Operators: Round and Round with Angular Momentum
        2. Finding Commutators of Lx, Ly, and Lz
        3. Creating the Angular Momentum Eigenstates
        4. Finding the Angular Momentum Eigenvalues
          1. Deriving eigenstate equations with βmax and βmin
          2. Getting rotational energy of a diatomic molecule
        5. Finding the Eigenvalues of the Raising and Lowering Operators
        6. Interpreting Angular Momentum with Matrices
        7. Rounding It Out: Switching to the Spherical Coordinate System
          1. The eigenfunctions of Lz in spherical coordinates
          2. The eigenfunctions of L2 in spherical coordinates
      2. Chapter 6: Getting Dizzy with Spin
        1. The Stern-Gerlach Experiment and the Case of the Missing Spot
        2. Getting Down and Dirty with Spin and Eigenstates
        3. Halves and Integers: Saying Hello to Fermions and Bosons
        4. Spin Operators: Running Around with Angular Momentum
        5. Working with Spin ½ and Pauli Matrices
          1. Spin ½ matrices
          2. Pauli matrices
    13. Part IV: Multiple Dimensions: Going 3D with Quantum Physics
      1. Chapter 7: Rectangular Coordinates: Solving Problems in Three Dimensions
        1. The Schrödinger Equation: Now in 3D!
        2. Solving Three-Dimensional Free Particle Problems
          1. The x, y, and z equations
          2. Finding the total energy equation
          3. Adding time dependence and getting a physical solution
        3. Getting Squared Away with 3D Rectangular Potentials
          1. Determining the energy levels
          2. Normalizing the wave function
          3. Using a cubic potential
        4. Springing into 3D Harmonic Oscillators
      2. Chapter 8: Solving Problems in Three Dimensions: Spherical Coordinates
        1. A New Angle: Choosing Spherical Coordinates Instead of Rectangular
        2. Taking a Good Look at Central Potentials in 3D
          1. Breaking down the Schrödinger equation
          2. The angular part of ψ(r, θ, ϕ)
          3. The radial part of ψ(r, θ, ϕ)
        3. Handling Free Particles in 3D with Spherical Coordinates
          1. The spherical Bessel and Neumann functions
          2. The limits for small and large ρ
        4. Handling the Spherical Square Well Potential
          1. Inside the square well: 0 < r < a
          2. Outside the square well: r > a
        5. Getting the Goods on Isotropic Harmonic Oscillators
      3. Chapter 9: Understanding Hydrogen Atoms
        1. Coming to Terms: The Schrödinger Equation for the Hydrogen Atom
        2. Simplifying and Splitting the Schrödinger Equation for Hydrogen
        3. Solving for ψ(R)
        4. Solving for ψ(r)
          1. Solving the radial Schrödinger equation for small r
          2. Solving the radial Schrödinger equation for large r
          3. You got the power: Putting together the solution for the radial equation
          4. Fixing f(r) to keep it finite
          5. Finding the allowed energies of the hydrogen atom
          6. Getting the form of the radial solution of the Schrödinger equation
          7. Some hydrogen wave functions
        5. Calculating the Energy Degeneracy of the Hydrogen Atom
          1. Quantum states: Adding a little spin
          2. On the lines: Getting the orbitals
        6. Hunting the Elusive Electron
      4. Chapter 10: Handling Many Identical Particles
        1. Many-Particle Systems, Generally Speaking
          1. Considering wave functions and Hamiltonians
          2. A Nobel opportunity: Considering multi-electron atoms
        2. A Super-Powerful Tool: Interchange Symmetry
          1. Order matters: Swapping particles with the exchange operator
          2. Classifying symmetric and antisymmetric wave functions
        3. Floating Cars: Tackling Systems of Many Distinguishable Particles
        4. Juggling Many Identical Particles
          1. Losing identity
          2. Symmetry and antisymmetry
          3. Exchange degeneracy: The steady Hamiltonian
          4. Name that composite: Grooving with the symmetrization postulate
        5. Building Symmetric and Antisymmetric Wave Functions
        6. Working with Identical Noninteracting Particles
          1. Wave functions of two-particle systems
          2. Wave functions of three-or-more-particle systems
        7. It's Not Come One, Come All: The Pauli Exclusion Principle
        8. Figuring out the Periodic Table
    14. Part V: Group Dynamics: Introducing Multiple Particles
      1. Chapter 11: Giving Systems a Push: Perturbation Theory
        1. Introducing Time-Independent Perturbation Theory
        2. Working with Perturbations to Nondegenerate Hamiltonians
          1. A little expansion: Perturbing the equations
          2. Matching the coefficients of λ and simplifying
          3. Finding the first-order corrections
          4. Finding the second-order corrections
        3. Perturbation Theory to the Test: Harmonic Oscillators in Electric Fields
          1. Finding exact solutions
          2. Applying perturbation theory
        4. Working with Perturbations to Degenerate Hamiltonians
        5. Testing Degenerate Perturbation Theory: Hydrogen in Electric Fields
      2. Chapter 12: Wham-Blam! Scattering Theory
        1. Introducing Particle Scattering and Cross Sections
        2. Translating between the Center-of-Mass and Lab Frames
          1. Framing the scattering discussion
          2. Relating the scattering angles between frames
          3. Translating cross sections between the frames
          4. Trying a lab-frame example with particles of equal mass
        3. Tracking the Scattering Amplitude of Spinless Particles
          1. The incident wave function
          2. The scattered wave function
          3. Relating the scattering amplitude and differential cross section
          4. Finding the scattering amplitude
        4. The Born Approximation: Rescuing the Wave Equation
          1. Exploring the far limits of the wave function
          2. Using the first Born approximation
          3. Putting the Born approximation to work
    15. Part VI: The Part of Tens
      1. Chapter 13: Ten Quantum Physics Tutorials
        1. An Introduction to Quantum Mechanics
        2. Quantum Mechanics Tutorial
        3. Grains of Mystique: Quantum Physics for the Layman
        4. Quantum Physics Online Version 2.0
        5. Todd K. Timberlake's Tutorial
        6. Physics 24/7's Tutorial
        7. Stan Zochowski's PDF Tutorials
        8. Quantum Atom Tutorial
        9. College of St. Benedict's Tutorial
        10. A Web-Based Quantum Mechanics Course
      2. Chapter 14: Ten Quantum Physics Triumphs
        1. Wave-Particle Duality
        2. The Photoelectric Effect
        3. Postulating Spin
        4. Differences between Newton's Laws and Quantum Physics
        5. Heisenberg Uncertainty Principle
        6. Quantum Tunneling
        7. Discrete Spectra of Atoms
        8. Harmonic Oscillator
        9. Square Wells
        10. Schrödinger's Cat
    16. Glossary
    17. Index

    Product information

    • Title: Quantum Physics For Dummies, Revised Edition
    • Author(s): Steven Holzner
    • Release date: January 2013
    • Publisher(s): For Dummies
    • ISBN: 9781118460887