Understanding the Quantum World

234 Pages·2019·18.97 MB·english

by  Erica W. Carlson

Topic Subtopic
An acclaimed physicist uses analogies to everyday life to teach the rules that govern
the microscopic world of particles in this accessible introduction to quantum theory. Science & Mathematics Physics
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Professor Erica W. Carlson
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Purdue University
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Erica W. Carlson is a Professor of Physics and Astronomy
at Purdue University. She holds a PhD in Physics from the
University of California, Los Angeles. Professor Carlson has
published dozens of research articles in peer-reviewed journals,
and her TEDx talk on emergence was well received among
both scientists and nonscientists. She was elected a fellow of
the American Physical Society and has received numerous
awards, including Purdue’s highest teaching award, the Charles
B. Murphy Outstanding Undergraduate Teaching Award.
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Erica W. Carlson, PhD
Professor of Physics and Astronomy
Purdue University
E
rica W. Carlson is a 150th Anniversary Professor and Professor of
Physics and Astronomy at Purdue University. She holds a BS in Physics
from the California Institute of Technology as well as a PhD in Physics from
the University of California, Los Angeles (UCLA). A theoretical physicist, she
researches electronic phase transitions in novel materials.
Prior to joining the faculty at Purdue, Professor Carlson did research in
theoretical condensed matter physics at Boston University. Her major
contributions have included spin excitations of electronic liquid crystal phases,
the prediction of a new phase of matter called a vortex smectic-A, and the
discovery of electronic fractals in strongly correlated electronic materials.
An award-winning teacher and researcher, Professor Carlson received
Research Corporation for Science Advancement’s Cottrell Scholar Award
and was elected a fellow of the American Physical Society “for theoretical
insights into the critical role of electron nematicity, disorder, and noise in
novel phases of strongly correlated electron systems and predicting unique
characteristics.” At UCLA, she won the teaching associate award from the
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Understanding the Quantum World
PROFESSOR BIOGRAPHY
Department of Physics and Astronomy. Professor Carlson has also received
numerous teaching awards as a faculty member at Purdue, including the
Ruth and Joel Spira Award for Excellence in Teaching (3 times); the College
of Science Award for Outstanding Contributions to Undergraduate
Teaching by an Assistant Professor; and Purdue’s highest teaching award,
the Charles B. Murphy Outstanding Undergraduate Teaching Award.
Professor Carlson has published dozens of research articles in peer-reviewed
journals and has presented her scientific work at numerous conferences and
invited talks on 4 continents. Her early experiments with podcasting college
science courses were featured on the front page of the Chicago Tribune.
She is active in outreach, having given science presentations to the public
as well as to students at various educational levels, ranging from preschool
through high school. Her TEDx talk on emergence was well received among
both scientists and nonscientists.
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Understanding the Quantum World
TABLE OF CONTENTS
TABLE OF
CONTENTS
INTRODUCTION
Professor Biography . . . . . . . . . . . . . . . . . . . . . . . . .i
Course Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
GUIDES
1 Particle-Wave Duality . . . . . . . . . . . . . . . . . 3
2 Particles, Waves, and Interference Patterns . . . . . 10
3 Observers Disturb What They Measure. . . . . . . 17
4 Bell’s Theorem and Schrödinger’s Cat. . . . . . . . 25
5 Quantum Paradoxes and Interpretations . . . . . . 32
6 The Position-Momentum Uncertainty Relation. . . . 40
7 Wave Quantization . . . . . . . . . . . . . . . . . 48
8 Quantum Wave Shapes and the Periodic Table . . 57
9 Interference of Waves and Sloshing States . . . . . 70
10 Wave Shapes in Diamond and Graphene . . . . . 80
11 Harmonic Oscillators . . . . . . . . . . . . . . . . 91
12 The Energy-Time Uncertainty Relation. . . . . . . .100
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Understanding the Quantum World
TABLE OF CONTENTS
13 Quantum Angular Momentum and Electron Spin . .108
14 Quantum Orbital Angular Momentum. . . . . . . . 115
15 Quantum Properties of Light . . . . . . . . . . . . . 124
16 Atomic Transitions and Photons . . . . . . . . . . . 133
17 Atomic Clocks and GPS. . . . . . . . . . . . . . . 141
18 Quantum Mechanics and Color Vision . . . . . . .148
19 A Quantum Explanation of Color . . . . . . . . . . 159
20 Quantum Tunneling . . . . . . . . . . . . . . . . .168
21 Fermions and Bosons . . . . . . . . . . . . . . . .180
22 Spin Singlets and the EPR Paradox . . . . . . . . . 187
23 Quantum Mechanics and Metals. . . . . . . . . .198
24 Superconductivity . . . . . . . . . . . . . . . . . .206
SUPPLEMENTARY MATERIAL
Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
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Understanding the Quantum World
COURSE SCOPE
UNDERSTANDING THE
QUANTUM WORLD
T
he microscopic world of particles—such as atoms, electrons, and
photons—is ruled by quantum mechanics. It’s a wild world where
particles become waves, waves become particles, and our understanding
of how physical objects behave is challenged to the core. This course
explores the fascinating findings scientists have uncovered about how
quantum particles operate.
The first segment of this course dives into the basic weirdness of quantum
phenomena: Based on measurements in laboratories, we know that small
particles like electrons can be in 2 places at once. You’ll learn how the
2-slit experiment reveals that even a single electron exhibits what’s called
interference effects when it has 2 possible paths it could follow. You’ll also
learn how this foundational experiment reveals both the particle and wave
nature of quantum objects.
The second segment of the course explores the meaning of these strange
findings. Can a particle really be in 2 places at once? Can Schrödinger’s
cat really be both dead and alive at the same time? The mathematics
of probabilities underlies much of quantum theory. Does this mean that
particles really behave in random ways, or do we use probabilities to
account for our own lack of knowledge? You’ll learn what scientists think
these probabilities mean and how to interpret Heisenberg’s uncertainty
principle for position/momentum and for energy/time.
The third segment of the course explores the physical consequences of
the idea that electrons are waves. Through analogies to physical systems
such as Slinkies and drumheads, you’ll gain an intuitive understanding of
the standing wave shapes that electrons take in atoms, molecules, and
materials. You’ll also learn how these beautiful geometric shapes determine
much of the structure in the periodic table of the elements as well as that of
molecules and materials.
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Understanding the Quantum World
COURSE SCOPE
The fourth segment of the course tackles the consequences of quantization
of energy and angular momentum. You’ll learn the strange behavior of
angular momentum at the quantum level, including what it means that
electrons and other quantum objects have quantized spin. You’ll also learn
how the photoelectric effect reveals that light—which was first thought to be
only a wave—is comprised of quantum particles known as photons.
In the final segment of the course, you’ll learn about the fundamental
quantum distinction between particles known as fermions and bosons
as well as about how fermions have been used to test the Einstein-
Podolsky-Rosen paradox. The course finishes by building on several of the
foundational quantum concepts presented earlier in the course in order to
explain why metals are metallic and why superconductors can conduct
electricity without losing energy.
Throughout the course, you will discover multiple applications of quantum
mechanics to your everyday life, including magnets, color vision and
lighting, and the exquisitely accurate quantum clocks that govern the global
positioning system (GPS). By the time you complete this course, you will
gain an appreciation for the incredible beauty and mystery that underlie
quantum phenomena, and you will gain an understanding of what we
know—and what we don’t yet know—about the quantum world.
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Lecture 1
Particle-Wave
01
Duality
T
he world of quantum mechanics is a world unlike the
one we observe every day. It’s a world of very small
objects—things like atoms, or the things inside of atoms,
that just don’t seem to play by the rules that apply to large
objects. In fact, some of the ideas in quantum mechanics
sound like they can’t possibly be true. For example,
consider particle-wave duality: Quantum mechanical
objects sometimes act like a wave and sometimes act like
a particle. But although such ideas seem strange and even
contradictory, learning the inner workings of quantum
physics will help resolve some of these paradoxes.
Scientists tend to prefer the language of mathematics and equations
to explain quantum physics because it is a much more precise
language than spoken languages, such as English.

Most of these lectures will not use any equations; instead, analogies
will be heavily relied on. But because analogies are rarely perfect,
there will be ambiguities.
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Understanding the Quantum World
LECTURE 1 Particle-Wave Duality
Are Particles Waves?
• Quantum mechanics is the world of the very tiny. It deals with things
about as small as atoms or smaller. So, atoms obey quantum mechanics;
the protons, neutrons, and electrons inside of atoms also obey quantum
mechanics; the things that make up protons and neutrons obey quantum
mechanics, too; and so on.
• In this tiny world, things aren’t always what they seem. It turns out that we
shouldn’t think of particles—such as protons and electrons—as tiny balls or
even as tiny points. When we look at such particles at the quantum level,
they look much more smeared out. In fact, at some level of zooming in on
such particles, they exhibit some properties that are very much like waves.
• Whatever these quantum objects are, they have some wave
properties and some particle properties. Here’s how you
can get started thinking about this conundrum: Picture a
wave that is not wiggling everywhere. To the right,
it’s flat and not wiggling. In the middle, there’s a
wavy portion, and then it flatlines again, and the
wave is not wiggling on the left.
• Here’s a key concept for waves
in quantum physics: Where the wave is not
wiggling and is flat, there is no chance of finding
the particle when you go to look for it—when you go
to measure its position. In the middle of the wiggly part,
where the wave is biggest, is where you’re most likely to find the particle.
In fact, the bigger the amplitude, or height, of the wave, the more likely
you are to find it in that spot. You’re less likely to find the particle on the
edge of the wiggly part, and there’s no chance of finding it where the
amplitude of the wave is zero, which is the flat part.
• So, if we take a wave that looks kind of like the one pictured above
and then shrink it down really small, it’s going to look like a particle to
you from a long distance. This is one way to think about how it could
be possible that something could be both a particle and a wave. That’s
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