Quantum
Physics FOR
REVISED EDITION
by Steven
Holzner
WILEY
John Wiley
& Sons, Inc.
Table of Contents Introduction
1
About This Book
1
Conventions Used in This Book
2
Foolish Assumptions How This Book Is Part I: Small
2
Organized
2
World, Huh? Essential Quantum Physics Handling Particles
3
Part II: Bound and Undetermined: in Bound States
3
Part III:
Turning to Angular Momentum and Spin Part IV: Multiple Dimensions: Going 3D with Quantum Physics Part V: Group Dynamics: Introducing Multiple Particles
3
Part VI: The Part of Tens
4
3 4
Icons Used in This Book
4
Where to Go from Here
5
Part 1: Small
Chapter 1:
World, Huh? Essential Quantum Physics
Discoveries and Essential Quantum
Being
Discrete: The Trouble with
Physics
Black-Body Radiation
7 9 10
First attempt: Wien's Formula Second attempt: Rayleigh-Jeans Law
12
An intuitive
12
(quantum) leap:
12
Max Planck's spectrum
The First Pieces: Seeing Light as Particles Solving the photoelectric effect
Scattering light Proof A Dual
off electrons: The
14
Compton effect
positron? Dirac and pair production
Identity: Looking
You Can't Know The
13
at Particles as
Waves
Everything (But You Can Figure the Odds) Quantum physics
and
17 18 20 20
Heisenberg uncertainty principle
Rolling the dice:
16
probability
Chapter 2: Entering the Matrix: Welcome to State Vectors Your Own Vectors in Hilbert
Creating 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
21
23 24 26 27 28 29
Quantum
Physics For Dummies, Revised Edition all your bases: Bras and kets
Covering
as
basis-less 30
state vectors kets
30
relationships using Understanding 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 some
Forward and Backward:
Finding
31 31 33
34 35
the Commutator
36 37
Commuting
Finding anti-Hermitian operators Starting from Scratch and Ending Up with
37
38
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
into
a
Stuck in
Handling
Energy Welts
57 59
in
potential wells Escaping from potential wells Trapping Particles in Infinite Square Potential Wells
Finding
a
wave-function
60 60
61 61
equation
Determining the energy levels Normalizing the wave function Adding time dependence to wave functions Shifting to symmetric square well potentials Limited Potential:
51
57
in Potential Wells
Binding particles
49
55
Square Well
Trapping Particles
46
52
Particles in Bound States
Looking
45
52
wave
Part 11: Bound and Undetermined:
Chapter 3: Getting
42
Taking
a
62 64 65 67
Look at Particles and Potential
Assuming the particle
has
plenty of energy Assuming the particle doesn't have enough
Steps
68 69
energy
Hitting the Wall: Particles and Potential Barriers Getting through potential barriers when E V0 Getting through potential barriers, even when E Particles Unbound: Solving the Schrodinger Equation
78
79
>
for Free Particles
Getting a physical particle with a wave packet Going through a Gaussian example
74
<
V0
81 85 87 88
Table of Contents
and Forth with Harmonic Oscillators
Chapter 4: Back
Grappling with the Harmonic Oscillator Hamiltonians Going
91
92
classical with harmonic oscillation
Understanding total energy in quantum oscillation Creation and Annihilation: Introducing the Harmonic Oscillator
93
94
Operators p's and q's: Getting the
Mind your
energy state equations
97
Finding
the harmonic oscillator energy
Putting
in
eigenstates
at Harmonic Oscillator
99 106
numbers
some
94 96
Finding the Eigenstates Using a and aT directly
Looking
91
Operators
as
Matrices
108
A Jolt of Java: Using Code to Solve the Schrodinger Equation 114
Numerically Making your approximations Building the actual code Running the code
Part 111:
Turning
to
114 116
123
Angular Momentum and Spin
125
Chapter 5: Working with Angular Momentum on
the Quantum Level
127
Ringing the Operators: Round and Round with Angular Momentum Finding Commutators of Lx, Ly, and Lz
128
Finding the Angular Momentum Eigenvalues Deriving eigenstate equations with Pmax and
133
Creating the Angular Momentum Eigenstates
Pmin
Getting rotational energy of a diatomic molecule Finding the Eigenvalues of the Raising and Lowering Operators Interpreting Angular
Rounding
It Out:
Momentum with Matrices
Switching
The
eigenfunctions
The
eigenfunctions of
to the
of L in \J in
Spherical
Coordinate System
130 131 133 136 138 139 146
coordinates
149
spherical coordinates
150
spherical
Chapter 6: Getting Dizzy with Spin The Stern-Gerlach Experiment and the Case of the Missing Spot Getting Down and Dirty with Spin and Eigenstates
157 157 159
Hello to Fermions and Bosons
160
Spin Operators: Running Around with Angular Momentum Working with Spin 'A and Pauli Matrices Spin '/2 matrices
161
Halves and
Integers: Saying
Pauli matrices
162
163 165
Quantum
Physics For
Dummies, Revised Edition
Part IV: Multiple bimensions: urith Quantum Physics
Goinq 30
Chapter 7: Rectangular Coordinates: Solving
167 Problems 169
in Three Dimensions
Schrodinger Equation: Now in 3D! Problems Solving Three-Dimensional Free Particle The x, y, and z equations Finding the total energy equation solution Adding time dependence and getting a physical Potentials 3D with Rectangular Getting Squared Away The
Determining the energy levels Normalizing the wave function
172
173 174 175
177 180
181 183
cubic potential
Using Springing into a
169
184
3D Harmonic Oscillators
Chapter 8: Solving Problems in Three Dimensions:
189
Spherical Coordinates Angle: Choosing Spherical Coordinates Instead of Rectangular Taking a Good Look at Central Potentials in 3D Breaking down the Schrodinger equation The angular part of i(/(r, 0, <|>) The radial part of \|/(r, 0, <|>) Handling Free Particles in 3D with Spherical Coordinates The spherical Bessel and Neumann functions The limits for small and large p Handling the Spherical Square Well Potential A New
Inside the square well: 0
a
Getting the Goods
on
Isotropic
192
192 193
194 195
196 197
198 199
200 201
Harmonic Oscillators
205
Chapter 9: Understanding Hydrogen Atoms Coming
190
to Terms: The
Schrodinger Equation Hydrogen Atom Simplifying and Splitting the Schrodinger Equation for Hydrogen
205
Solving for \]/(R)
210
for the
Solving
for
211
y(r) for small
Solving the radial Schrodinger equation Solving the radial Schrodinger equation for large You got the power: Putting together the solution the radial
Fixing
208
equation keep it finite allowed energies
r
211
r
212
for
f(r) to
212 215
of the hydrogen atom Finding the Getting the form of the radial solution of the Schrodinger equation
216
Some
220
hydrogen wave functions
218
Table of Contents
Calculating the Energy Degeneracy of the Hydrogen Atom Quantum states: Adding a little spin On the lines: Getting the orbitals Hunting the Elusive Electron
Chapter 10: Handling Many Identical
Particles
Cars:
235 235
wave
functions
of
Particles
Floating Tackling Systems Many Distinguishable Juggling Many Identical Particles Losing identity Symmetry and antisymmetry Exchange degeneracy: The steady Hamiltonian Name that composite: Grooving with the symmetrization and
Antisymmetric
Wave Functions
with Identical Noninteracting Particles
Wave functions of
Part V:
237 239
242 242 244 244 245
postulate Working
233
Swapping particles with
symmetric and antisymmetric
Building Symmetric
228
232 atoms
exchange operator
Classifying
226
232
Considering wave functions and Hamiltonians A Nobel opportunity: Considering multi-electron A Super-Powerful Tool: Interchange Symmetry the
224
231
Many-Particle Systems, Generally Speaking
Order matters:
222
two-particle systems
246
247 248
Wave functions of three-or-more-particle systems It's Not Come One, Come All: The Pauli Exclusion Principle
249
Figuring out the Periodic Table
251
Group Dynamics: Introducing
Multiple Particles
Chapter 11: 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 A. and simplifying
250
253 255 255 256 257 258
Finding the first-order corrections
259
Finding
261
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
Chapter 12: Wham-Blam! Scattering Theory Introducing Particle Scattering and Cross Sections
262 264 264 269 271
275 275
Quantum
Physics
For Dummies, Revised Edition
277
and Lab Frames Translating between the Center-of-Mass Framing the scattering discussion the scattering angles between frames
Relating Translating cross sections between the frames of equal Trying a lab-frame example with particles Particles of Spinless the Amplitude Scattering Tracking
277 278
281 mass
The incident wave function
Relating the scattering amplitude
285
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
An Introduction to
Quantum
Physics Tutorials
Quantum
288 289
290 291
Grains of Mystique: Quantum Physics Quantum Physics Online Version 2.0
295 295
Mechanics
295
Mechanics Tutorial
for the Layman
.296 296 296
Todd K. Timberlake's Tutorial
Physics 24/7's
286
293
of Tens
13: Ten Quantum
284
and differential
cross section
Chapter
283 285
The scattered wave function
Part VI: The Part
282
296
Tutorial
Stan Zochowski's PDF Tutorials
297
Quantum Atom Tutorial College of St. Benedict's Tutorial A Web-Based Quantum Mechanics Course
297
Chapter 14: Ten Quantum Physics Triumphs Wave-Particle
297
297
299 299
Duality
The Photoelectric Effect
299
Postulating Spin
300
Differences between Newton's Laws and
Quantum Physics
300
Heisenberg Uncertainty Principle Quantum Tunneling Discrete Spectra of Atoms
300
Harmonic Oscillator
301
Square Wells
302
Schrodinger's Cat
302
301
301
Glossary
303
Index
309
