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BOB FIELD: I'm Bob Field.

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This is my 44th year
at MIT, and I've

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taught this course
roughly half the time,

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so it is my favorite course.

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And I'm a
spectroscopist, and that

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means that I use
quantum mechanics

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almost like breathing.

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And I'm going to try to convey
some of the beauty and utility

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of quantum mechanics.

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This is not a typical
undergraduate quantum mechanics

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class.

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It's not about history.

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It's not about philosophy.

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It's about use-- use
for understanding

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complicated stuff,
use for insight.

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And so a lot of
the material is not

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in the assigned text,
which is a very good book,

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but it's mostly a safety net.

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The printed notes, all of which
are posted except for a few

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lectures that I'm
still working on--

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and that is the text.

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Everything in the notes,
you're responsible for.

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There are sections of the
notes which I call non-lecture.

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That's explanation of what's
in the lecture or a little bit

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going beyond it.

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00:01:37,250 --> 00:01:39,260
You're responsible for that.

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If I don't finish all the
material in the notes,

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you're responsible for the
material I didn't finish.

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00:01:45,650 --> 00:01:47,570
You can ask me
questions about it.

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00:01:47,570 --> 00:01:50,280
You can ask your TAs
questions about it.

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00:01:50,280 --> 00:01:56,390
But there's a
supplementary text,

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00:01:56,390 --> 00:01:59,140
which is a book
that I wrote which

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is intended to take
undergraduates like you

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00:02:04,910 --> 00:02:09,289
to the frontier of
research in spectroscopy.

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This is the book that I used to
use to teach graduate quantum

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mechanics.

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So I've written a lot of
stuff which is already

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available on the
web, but I just want

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to make sure that you know
the structure of the course.

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00:02:24,860 --> 00:02:28,880
There are going to be nine
problem sets, always in weeks

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there is not an exam--

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when there is not an exam.

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00:02:33,170 --> 00:02:37,610
And the problem sets
are worth 100 points.

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00:02:37,610 --> 00:02:41,380
There will be three
50-minute exams, to which you

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will be allotted 90 minutes.

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And they'll be evening exams
and on Thursday nights.

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OK, there will be a final
during final exam period.

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And so the points for
the course add up to 600.

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For each exam, you will be
entitled to bring one 8 1/2

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by 11 page that you've prepared
with as dense or as coarse

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writing as you want--

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a different one page, only
one page, for each exam

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and for the final.

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One page-- the exam--

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one page for the exam.

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One page for the final.

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Not four pages
for the final, not

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two pages for the
second exam, et cetera--

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one page.

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I believe that writing these
pages of notes or pages

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of things you should
remember provide structure

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that you actually learn
by preparing this,

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and so I stick to this.

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My job here is to
force you to suspend

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what you expect about the
way matter and light behave.

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You expect things based
on your experience

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with macroscopic objects,
and you're very smart.

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You're here at MIT
because you are

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able to integrate
those expectations

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and to express them in
mathematical analysis

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of your observations.

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So you're pretty good at that.

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But quantum mechanics
forces you to step away

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from what you think you
understand perfectly

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because it doesn't apply
in microscopic systems.

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And so I'm going to destroy your
expectations about how things

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work at the beginning,
and by the end,

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I will give them back
to you in the form

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of things called wave packets.

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Wave packets are quantum
mechanical particle-like

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objects.

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They obey the rules, and they do
a lot of the things you expect.

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But initially, you
have to suspend

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that belief in particles.

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OK, so I'm going to start by
throwing a piece of chalk.

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I have to throw it at my TAs.

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So here is a piece of
chalk, and the chalk

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followed a trajectory.

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If you're a major
league outfielder,

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you look at the initial
part of a trajectory,

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and you can pretty much figure
out where you have to go.

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This sort of thing would
be the subject of 801,

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00:05:47,320 --> 00:05:49,450
but the outfielders
don't know physics.

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They just have
instincts, and they

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know that if they look at the
beginning of a trajectory,

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they can predict where it
will end and when it will end,

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and this is really important.

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That's the macroscopic view.

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We talk about trajectories.

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In quantum mechanics,
there are no trajectories.

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We have possibly an
observation of what

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was the initial condition and
what was the detection event,

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but we can't describe
what's going on

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by observing, point by point,
the position and momentum.

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We're only allowed to do what
we call click-click experiments.

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We start something in some
kind of a well-prepared state,

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and then we detect what
has happened at the end.

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We might do something to
the system in between,

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but we cannot observe everything
as the system evolves.

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And here, I will
attempt to a little bit

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justify that you need to
suspend what you believe.

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I threw a piece of chalk.

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It could have been a baseball.

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And suppose now I
said, let's decrease

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the mass of the thrower, the
catcher, and the object by 100.

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You pretty much know
exactly what will happen.

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Now let's decrease
it by a factor of 10

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to the 20, which is like going
from a baseball to an electron.

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You think you might know, but
I guarantee you don't know.

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And you're going
to be surprised,

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and it's because in
the microscopic world,

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observation modifies
the state of the system,

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and any sort of interaction
of the evolving system

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is going to affect
what you observe.

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And so we have to create a
formal structure, which is

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a kind of measurement theory.

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What measurements are
we allowed to make,

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and what do they tell us?

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Because you cannot observe
the time dependence.

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You can calculate what the
time dependence is if you know

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enough, but you cannot observe
the thing evolving except

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by destroying it.

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OK, so quantum
mechanics is beautiful

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because it describes
the microscopic world,

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and it doesn't tell
you you're wrong

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about the macroscopic world.

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It matches everything the
macroscopic world does.

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OK, some of the key ideas
of quantum mechanics--

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so you do a series of
identical experiments.

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You don't get the same
result. It's probabilistic,

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and that should bother
you because if you

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do an experiment
carefully, you're

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trained to think that
you do it carefully,

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you'll get the same result.
But quantum mechanics says,

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tough luck.

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You can't do an
experiment that carefully.

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There's also this
wave-particle duality.

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You know what particles
are and what the properties

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of particles are.

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You learn that in 8.01.

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You know what waves are, and
you probably also learned

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00:10:08,500 --> 00:10:11,350
that in 8.01 or 8.02.

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But you know instinctively
that particles and waves

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behave differently.

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But in quantum
mechanics, everything

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is both particle-like
and wave-like,

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and this is also something
that should bother you.

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And the third thing is
energy quantization.

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Now, I said I'm
a spectroscopist,

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so I live and die by
these spectra, which

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consist of transitions
between energy levels.

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And these transitions
between energy levels

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encode everything
we want to know

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about the mechanics
of an object--

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its structure, what it does.

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And so quantum mechanics
is an elaborate encoder

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of information, and
it's usually encoded

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in the form of these
quantized energy levels.

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And so you're
going to want to be

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able to calculate how the energy
levels or the spectrum that you

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would observe for an object
is related to the thing that

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describes what it can do.

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00:11:30,560 --> 00:11:34,000
And that's the Hamiltonian,
and the Hamiltonian we'll

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00:11:34,000 --> 00:11:36,860
look at in many useful ways.

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Now, I just want to
warn you that there

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are two ways of
presenting quantum

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mechanics-- the Schrodinger
picture, which is differential

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00:11:48,250 --> 00:11:51,900
equations and wave
functions, and the Heisenberg

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00:11:51,900 --> 00:11:55,830
picture, which is
matrix mechanics, where

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we have matrices and
we have eigenvectors.

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00:12:00,330 --> 00:12:06,180
And I am an advocate.

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00:12:06,180 --> 00:12:12,260
I'm passionate about the matrix
picture because what it does

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00:12:12,260 --> 00:12:15,740
is presents everything in
a way that you can then

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organize your insights, whereas
the Schrodinger picture mostly

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involves solving one
complicated differential

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00:12:23,750 --> 00:12:28,280
equation after another, and the
focus is on the mathematics,

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00:12:28,280 --> 00:12:31,280
and it's much harder
to see the big picture.

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Now, that means you need to know
a little bit of linear algebra.

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00:12:35,790 --> 00:12:38,640
Now, most of you haven't taken
a course in linear algebra,

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but that doesn't matter because
the amount of linear algebra

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you need to know for quantum
mechanics is extremely small,

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00:12:45,680 --> 00:12:49,250
and I will probably present
all of it in lectures.

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00:12:49,250 --> 00:12:55,790
But you will definitely
have the TAs as a resource,

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00:12:55,790 --> 00:13:00,500
and it's possible that they
will give some formal lectures

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00:13:00,500 --> 00:13:03,380
on linear algebra
or some handouts,

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00:13:03,380 --> 00:13:06,240
but it's not complicated.

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00:13:06,240 --> 00:13:08,370
It's beautiful.

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00:13:08,370 --> 00:13:18,400
OK, so light.

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Light is electromagnetic
radiation.

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00:13:28,420 --> 00:13:30,680
You've heard that.

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00:13:30,680 --> 00:13:34,390
And it is both wave-like
and particle-like.

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00:13:34,390 --> 00:13:39,370
Now, the particle-like aspect
of light is going to bother you,

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00:13:39,370 --> 00:13:42,520
but it's very easy to
show that it's necessary.

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00:13:42,520 --> 00:13:49,250
OK, so first of all, what are
some wave characteristics?

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00:13:52,260 --> 00:13:59,194
If you have a wave, what
kind of measurements

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00:13:59,194 --> 00:14:00,360
are you going to make on it?

214
00:14:05,850 --> 00:14:06,970
OK, Sasha.

215
00:14:06,970 --> 00:14:10,160
AUDIENCE: Intensity
at a point in space.

216
00:14:10,160 --> 00:14:12,610
BOB FIELD: There can be
intensity at a point in space,

217
00:14:12,610 --> 00:14:15,130
but there could also be
particles that are impinging

218
00:14:15,130 --> 00:14:18,780
on that point, so you need
something a little bit more

219
00:14:18,780 --> 00:14:22,330
that is definitely
wave-like, and you have--

220
00:14:22,330 --> 00:14:23,120
yes?

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00:14:23,120 --> 00:14:25,845
AUDIENCE: It has a frequency and
a wavelength and an amplitude.

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00:14:25,845 --> 00:14:26,470
BOB FIELD: Yes.

223
00:14:30,780 --> 00:14:34,590
I'm angling for
something more, but it

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00:14:34,590 --> 00:14:37,080
does have a frequency
and a wavelength,

225
00:14:37,080 --> 00:14:43,730
and wavelengths are
how you understand

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00:14:43,730 --> 00:14:44,630
interference effects.

227
00:14:47,750 --> 00:14:57,520
And when you put light through
a lens, there's refraction.

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00:14:57,520 --> 00:15:00,330
When you put light
on a grating, there's

229
00:15:00,330 --> 00:15:03,180
diffraction-- or
through a pinhole.

230
00:15:03,180 --> 00:15:06,420
And there's the
two-slit experiment,

231
00:15:06,420 --> 00:15:12,690
where you send light on an
object which has two slits,

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00:15:12,690 --> 00:15:16,020
and you can't tell which
slit the light went through.

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00:15:16,020 --> 00:15:18,870
This is a very beautiful
thing which I will talk about

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00:15:18,870 --> 00:15:22,570
in a coming lecture--

235
00:15:22,570 --> 00:15:24,720
in fact, lecture number three.

236
00:15:24,720 --> 00:15:31,500
So the key properties of waves
are refraction, diffraction,

237
00:15:31,500 --> 00:15:33,190
two-slit experiment.

238
00:15:33,190 --> 00:15:36,160
And behind that is
interference effects.

239
00:15:44,120 --> 00:15:50,810
So we can have just a comic
book picture or a cartoon.

240
00:15:50,810 --> 00:15:55,730
So here is a wave, and
here is another wave.

241
00:15:55,730 --> 00:16:01,370
And this other wave has exactly
the same frequency and phase.

242
00:16:01,370 --> 00:16:03,860
And if we add these
two guys together,

243
00:16:03,860 --> 00:16:08,610
we get something
that looks like that.

244
00:16:08,610 --> 00:16:14,150
And in fact, the addition
is a little bit nonlinear.

245
00:16:14,150 --> 00:16:17,280
So we have constructive
interference,

246
00:16:17,280 --> 00:16:26,610
or we can have destructive
interference and anything

247
00:16:26,610 --> 00:16:27,810
in between.

248
00:16:27,810 --> 00:16:31,950
If we add these two guys,
what you get is nothing.

249
00:16:31,950 --> 00:16:36,090
So here, you get an intensified
wave-- constructive.

250
00:16:36,090 --> 00:16:39,640
And here, we get cancellation.

251
00:16:39,640 --> 00:16:41,910
Now, it's a little
bit stressful to think

252
00:16:41,910 --> 00:16:44,400
that if particles have
wave characteristics,

253
00:16:44,400 --> 00:16:50,072
they can annihilate
each other, so you'll

254
00:16:50,072 --> 00:16:51,280
have to be prepared for that.

255
00:16:53,810 --> 00:17:00,580
So quantum mechanics exploits
constructive and destructive

256
00:17:00,580 --> 00:17:01,240
interference.

257
00:17:01,240 --> 00:17:05,560
That's at the core, and you
have to get used to that,

258
00:17:05,560 --> 00:17:08,599
and you have to get used to
seeing particles do that.

259
00:17:12,460 --> 00:17:21,500
OK, so waves have a
frequency and a velocity

260
00:17:21,500 --> 00:17:23,940
and a wavelength.

261
00:17:23,940 --> 00:17:27,835
And now here, what is nu?

262
00:17:27,835 --> 00:17:29,330
Nu is c over lambda.

263
00:17:32,080 --> 00:17:35,560
If someone on the
telephone or on Skype

264
00:17:35,560 --> 00:17:38,200
constantly asks
you "what is new,"

265
00:17:38,200 --> 00:17:39,880
you can put an end
to that behavior

266
00:17:39,880 --> 00:17:43,720
by saying c over lambda.

267
00:17:43,720 --> 00:17:46,010
And if you do it often
enough, it'll stop.

268
00:17:48,590 --> 00:17:51,080
It may be that the
question will be rephrased,

269
00:17:51,080 --> 00:17:56,030
but it's useful to remember
this as a repellent and also

270
00:17:56,030 --> 00:17:58,462
as a crucial
organizing principle.

271
00:18:01,360 --> 00:18:05,590
OK, waves are
electromagnetic, and so that

272
00:18:05,590 --> 00:18:11,520
means we have transverse
electromagnetic waves.

273
00:18:11,520 --> 00:18:17,080
And so here is one
part of the wave,

274
00:18:17,080 --> 00:18:20,380
and here is another
part of the wave.

275
00:18:23,190 --> 00:18:27,330
And this is the electric
part of the wave.

276
00:18:27,330 --> 00:18:33,540
And so we have zero,
and here is E0.

277
00:18:33,540 --> 00:18:41,710
And this is the magnetic part
of the wave, zero and B0.

278
00:18:41,710 --> 00:18:46,410
And this is in the xz plane.

279
00:18:46,410 --> 00:18:48,710
This is the z direction.

280
00:18:48,710 --> 00:18:50,510
This is the z direction.

281
00:18:50,510 --> 00:18:53,940
And this is the yz plane.

282
00:18:53,940 --> 00:18:56,550
Now, this corresponds to
a wave which is linearly

283
00:18:56,550 --> 00:19:00,030
polarized along the x-axis.

284
00:19:00,030 --> 00:19:04,400
And so this is-- it's kind
of hard to draw a transverse

285
00:19:04,400 --> 00:19:06,980
electromagnetic wave, but
there's an electric part

286
00:19:06,980 --> 00:19:08,210
and a magnetic part.

287
00:19:08,210 --> 00:19:11,855
And for the most part,
I forget about this.

288
00:19:11,855 --> 00:19:15,150
The magnetic resonance-- this is
the only thing you care about,

289
00:19:15,150 --> 00:19:20,590
but they're both part of light.

290
00:19:20,590 --> 00:19:23,730
And OK.

291
00:19:23,730 --> 00:19:30,690
So we have these waves, and
now, the intensity of the light

292
00:19:30,690 --> 00:19:38,070
is proportional to
the E0 squared--

293
00:19:38,070 --> 00:19:41,430
the electric field squared.

294
00:19:41,430 --> 00:19:48,020
And it's also measured in
watts per square centimeter.

295
00:19:48,020 --> 00:19:49,340
And this is in--

296
00:19:49,340 --> 00:19:53,120
so this is in volts
per centimeter squared.

297
00:19:53,120 --> 00:19:55,610
Now, I'm an old fashioned guy.

298
00:19:55,610 --> 00:19:57,690
I use centimeters
instead of meters.

299
00:19:57,690 --> 00:20:03,110
You'll just have to forgive me
for that, not using MKS units.

300
00:20:03,110 --> 00:20:06,230
But the important thing
is that the intensity

301
00:20:06,230 --> 00:20:09,140
is related to the square
of an electric field.

302
00:20:13,240 --> 00:20:18,060
So suppose we have light
impinging on a hunk of metal.

303
00:20:23,260 --> 00:20:25,420
So a metal is something
where the electrons are

304
00:20:25,420 --> 00:20:30,850
free to move around, and so we
like a metal because of that.

305
00:20:30,850 --> 00:20:33,820
We could ask, well, what
happens if we put light

306
00:20:33,820 --> 00:20:39,190
on salt or on some
organic molecule?

307
00:20:39,190 --> 00:20:43,540
And in some sense, there is
going to be a relationship,

308
00:20:43,540 --> 00:20:51,020
but the easy thing is if we put
a beam of light onto a metal

309
00:20:51,020 --> 00:20:52,740
and it's pushing the
electrons around.

310
00:20:52,740 --> 00:20:55,040
That's what an
electric field does.

311
00:20:55,040 --> 00:20:56,810
It moves the electrons.

312
00:20:56,810 --> 00:21:02,090
And so you would
expect classically

313
00:21:02,090 --> 00:21:04,700
that at high enough
intensity, you're

314
00:21:04,700 --> 00:21:09,760
going to start ripping
electrons out of the metal,

315
00:21:09,760 --> 00:21:12,610
and that would be wrong.

316
00:21:12,610 --> 00:21:14,350
And this is the
photoelectric effect.

317
00:21:17,271 --> 00:21:18,270
This is what we observe.

318
00:21:21,610 --> 00:21:26,490
0-- the current divided by
the charge of the electron.

319
00:21:26,490 --> 00:21:29,400
So that's the number of
electrons per second,

320
00:21:29,400 --> 00:21:32,930
and this is the intensity.

321
00:21:32,930 --> 00:21:37,460
And if we have
infrared radiation,

322
00:21:37,460 --> 00:21:42,820
nothing happens, no
matter how strong it is.

323
00:21:42,820 --> 00:21:46,360
If we have
ultraviolet radiation,

324
00:21:46,360 --> 00:21:49,120
we have something happening.

325
00:21:49,120 --> 00:21:53,320
As the intensity of
the light increases,

326
00:21:53,320 --> 00:22:00,610
the number of electrons per
second ejected from the metal

327
00:22:00,610 --> 00:22:03,050
increases linearly.

328
00:22:03,050 --> 00:22:04,120
So why is that?

329
00:22:04,120 --> 00:22:08,230
We expect that it would be
intensity that determines it,

330
00:22:08,230 --> 00:22:12,580
but it's the color of the
light that determines.

331
00:22:12,580 --> 00:22:18,740
We can also do something
like this, where we again

332
00:22:18,740 --> 00:22:23,060
ask, what is the current divided
by the charge of the electron

333
00:22:23,060 --> 00:22:25,370
versus frequency?

334
00:22:25,370 --> 00:22:27,720
And again, we have 0 here.

335
00:22:27,720 --> 00:22:32,330
And what we see is nothing
up until some critical point,

336
00:22:32,330 --> 00:22:34,010
and then this is--

337
00:22:34,010 --> 00:22:37,700
so this is some special
frequency, which

338
00:22:37,700 --> 00:22:41,710
is different for every metal.

339
00:22:41,710 --> 00:22:46,650
And then, all of a sudden,
we start getting electrons.

340
00:22:46,650 --> 00:22:54,630
And this increases linearly,
or at least for a while

341
00:22:54,630 --> 00:22:56,790
increases linearly
with the frequency.

342
00:22:59,820 --> 00:23:02,250
So there's something about
the frequency of light

343
00:23:02,250 --> 00:23:04,080
that rips out the electrons.

344
00:23:04,080 --> 00:23:06,060
It has to be above
a certain minimum,

345
00:23:06,060 --> 00:23:12,150
and then the electrons
increase with the frequency,

346
00:23:12,150 --> 00:23:15,180
but in a little bit more
complicated way than linearly.

347
00:23:15,180 --> 00:23:18,450
And so I have something in the
notes which is not quite right,

348
00:23:18,450 --> 00:23:21,241
but this onset is important.

349
00:23:24,130 --> 00:23:28,360
So these observations
suggest that the electron

350
00:23:28,360 --> 00:23:37,270
is bound to the metal by some
energy which we call the work

351
00:23:37,270 --> 00:23:41,760
function, and it's called phi.

352
00:23:41,760 --> 00:23:47,770
And so this is the energy that
it takes to rip an electron out

353
00:23:47,770 --> 00:23:49,390
of a metal.

354
00:23:49,390 --> 00:23:51,160
And so it's called
the work function,

355
00:23:51,160 --> 00:23:52,800
and work functions
for metals range

356
00:23:52,800 --> 00:23:55,420
from a little over
1 electron volt

357
00:23:55,420 --> 00:24:00,480
to around 5 electron volts.

358
00:24:00,480 --> 00:24:01,870
I'm going to use those units.

359
00:24:01,870 --> 00:24:03,170
Well, you can forget that.

360
00:24:03,170 --> 00:24:08,260
But all metals are within
a relatively narrow range

361
00:24:08,260 --> 00:24:16,650
of work functions, and this
is somehow related to nu 0.

362
00:24:16,650 --> 00:24:20,740
So this is an energy,
and this is a frequency.

363
00:24:20,740 --> 00:24:26,400
And so we expect that there is
some relationship between nu

364
00:24:26,400 --> 00:24:31,080
0 and this energy, and there is
some proportionality concept,

365
00:24:31,080 --> 00:24:33,650
which I can call
anything I want,

366
00:24:33,650 --> 00:24:36,060
but I'm going to call
it h because it's going

367
00:24:36,060 --> 00:24:39,010
to become Planck's constant.

368
00:24:39,010 --> 00:24:40,860
That's the
proportionality concept.

369
00:24:40,860 --> 00:24:46,900
And so the onset of
ejection of electrons

370
00:24:46,900 --> 00:24:49,630
is when the
frequency of light is

371
00:24:49,630 --> 00:24:51,310
greater than the work function.

372
00:24:56,640 --> 00:24:59,635
As I said, every metal has
a different work function.

373
00:25:05,140 --> 00:25:11,390
OK, so this is
looking like somehow,

374
00:25:11,390 --> 00:25:20,760
the light does not act in an
additive way on the metal.

375
00:25:20,760 --> 00:25:24,160
It acts in a
singular way somehow.

376
00:25:24,160 --> 00:25:27,640
There are particles of light
that have definite energy.

377
00:25:27,640 --> 00:25:29,400
This is what it
looks like, and we're

378
00:25:29,400 --> 00:25:33,370
going to call those
particles of light photons.

379
00:25:33,370 --> 00:25:35,510
And so now we're
trying to think of,

380
00:25:35,510 --> 00:25:44,280
all right, electromagnetic
radiation comes as particles.

381
00:25:44,280 --> 00:25:46,650
What are the properties
of particles?

382
00:25:50,370 --> 00:25:59,120
Well, particles-- well, I'm
getting ahead of myself,

383
00:25:59,120 --> 00:26:01,210
but as long as I
said this, particles

384
00:26:01,210 --> 00:26:07,870
have kinetic energy
and momentum.

385
00:26:07,870 --> 00:26:09,970
Kinetic energy is
a scalar quantity.

386
00:26:09,970 --> 00:26:12,250
Momentum is a vector quantity.

387
00:26:12,250 --> 00:26:18,150
And right now,
what we want to do

388
00:26:18,150 --> 00:26:22,770
is measure the kinetic energy of
the electrons that are produced

389
00:26:22,770 --> 00:26:26,280
by the annihilation of photons.

390
00:26:26,280 --> 00:26:29,910
OK, and so we can imagine
an apparatus like this.

391
00:26:29,910 --> 00:26:33,630
Here is our metal, and
here is the light impinging

392
00:26:33,630 --> 00:26:34,740
on the metal.

393
00:26:34,740 --> 00:26:38,730
And we have grids.

394
00:26:38,730 --> 00:26:48,335
We have a ground, and we have
another grid and a detector.

395
00:26:52,356 --> 00:27:05,230
So we have ground voltage is 0.

396
00:27:05,230 --> 00:27:08,930
Here we have a
voltage less than 0.

397
00:27:08,930 --> 00:27:12,310
Electrons don't like that.

398
00:27:12,310 --> 00:27:16,100
But these two grids are
at the same potential.

399
00:27:16,100 --> 00:27:20,890
So the electrons don't
know which way to go.

400
00:27:20,890 --> 00:27:25,570
And then there's another
grid where we have

401
00:27:25,570 --> 00:27:29,680
the potential is V plus V stop.

402
00:27:33,390 --> 00:27:37,940
And so what happens is if the
electron is ejected with enough

403
00:27:37,940 --> 00:27:41,810
kinetic energy to
go uphill and cross

404
00:27:41,810 --> 00:27:46,730
through this potential,
this grid, then

405
00:27:46,730 --> 00:27:51,860
it will make it to the
detector and we'll count it.

406
00:27:51,860 --> 00:27:55,600
So this is just a
crude apparatus.

407
00:27:55,600 --> 00:27:57,650
If you were going to
do this experiment,

408
00:27:57,650 --> 00:28:00,510
you would probably
design it better.

409
00:28:00,510 --> 00:28:02,720
But the idea is
what we want to do

410
00:28:02,720 --> 00:28:07,520
is to measure what is
the voltage that we

411
00:28:07,520 --> 00:28:11,135
apply that causes the electrons
to stop reaching the detector.

412
00:28:15,370 --> 00:28:17,400
And that's the way we
measure the kinetic energy

413
00:28:17,400 --> 00:28:19,410
of the electrons.

414
00:28:19,410 --> 00:28:22,980
When all of the electrons
stop hitting the detector,

415
00:28:22,980 --> 00:28:27,160
we know the voltage,
the stopping voltage.

416
00:28:27,160 --> 00:28:32,222
And we can now plot
the stopping voltage.

417
00:28:32,222 --> 00:28:33,120
V stop.

418
00:28:44,220 --> 00:28:48,090
Versus frequency.

419
00:28:48,090 --> 00:28:50,160
And here is nu 0.

420
00:28:50,160 --> 00:28:52,770
And what we see is this.

421
00:28:52,770 --> 00:28:59,010
We see that below nu 0, there
are no electrons ejected.

422
00:28:59,010 --> 00:29:03,990
Once we're above nu 0,
electrons start being ejected.

423
00:29:03,990 --> 00:29:07,800
And they have a kinetic energy,
which is measured by V stop.

424
00:29:07,800 --> 00:29:12,370
And it increases
linearly with frequency.

425
00:29:12,370 --> 00:29:16,570
Now, when we do this
experiment on different metals,

426
00:29:16,570 --> 00:29:19,450
the slope is constant, the same.

427
00:29:19,450 --> 00:29:21,650
It's universal.

428
00:29:21,650 --> 00:29:28,450
So the kinetic energy
of the ejected electrons

429
00:29:28,450 --> 00:29:30,505
is equal to some constant.

430
00:29:33,730 --> 00:29:36,730
It goes as minus nu 0.

431
00:29:36,730 --> 00:29:40,790
And this is the same
constant that we saw before.

432
00:29:40,790 --> 00:29:42,590
And this is Planck's constant.

433
00:29:42,590 --> 00:29:48,010
And now what we've seen is
that these particles of light

434
00:29:48,010 --> 00:29:51,040
have definite energy.

435
00:29:51,040 --> 00:29:53,050
They have definite
kinetic energy.

436
00:29:53,050 --> 00:29:58,300
And we can stop and they
transfer that energy.

437
00:30:01,520 --> 00:30:04,910
And so we can draw an
energy level diagram.

438
00:30:04,910 --> 00:30:14,360
So here's 0 and here.

439
00:30:14,360 --> 00:30:16,190
So this is energy.

440
00:30:16,190 --> 00:30:19,550
And this is minus
the work function.

441
00:30:19,550 --> 00:30:25,650
And so we have a photon,
which has this energy.

442
00:30:25,650 --> 00:30:30,930
And we have the kinetic
energy of the electrons.

443
00:30:38,680 --> 00:30:44,120
And this is h nu minus h nu 0.

444
00:30:44,120 --> 00:30:45,010
OK.

445
00:30:45,010 --> 00:30:47,360
This story is complete.

446
00:30:47,360 --> 00:30:50,450
The photoelectron effect
is the easiest thing

447
00:30:50,450 --> 00:30:55,540
to understand at the beginning
of quantum mechanics.

448
00:30:55,540 --> 00:30:59,030
And it says that light
comes in particles,

449
00:30:59,030 --> 00:31:00,800
which we call photons.

450
00:31:00,800 --> 00:31:05,610
And the energy of
a photon is h nu.

451
00:31:05,610 --> 00:31:08,270
h is a fundamental constant.

452
00:31:08,270 --> 00:31:10,800
And we know what nu is.

453
00:31:13,341 --> 00:31:13,840
OK.

454
00:31:19,120 --> 00:31:22,090
I'm going to talk about
Compton scattering.

455
00:31:22,090 --> 00:31:26,620
But Compton scattering
is a little bit harder

456
00:31:26,620 --> 00:31:30,250
to understand than the
photoelectron effect.

457
00:31:30,250 --> 00:31:32,950
And I'm going to put
equations on the board which

458
00:31:32,950 --> 00:31:34,120
I'm not going to derive.

459
00:31:34,120 --> 00:31:36,280
They're easily derived.

460
00:31:36,280 --> 00:31:39,910
But this is just to
complete the picture

461
00:31:39,910 --> 00:31:45,850
of the particle-like
characteristic of Planck.

462
00:31:50,050 --> 00:31:58,950
So for Compton scattering,
we have a beam of x-rays.

463
00:32:02,180 --> 00:32:04,010
X-ray is a form of light.

464
00:32:04,010 --> 00:32:06,500
It's a very high
energy form of light.

465
00:32:06,500 --> 00:32:08,405
We have a block of paraffin.

466
00:32:13,020 --> 00:32:20,520
And what we observe is there
are electrons kicked out.

467
00:32:24,270 --> 00:32:30,248
And there is x-ray scattered.

468
00:32:33,000 --> 00:32:36,540
So the experiment is we're
looking for the particle

469
00:32:36,540 --> 00:32:37,950
characteristics.

470
00:32:37,950 --> 00:32:42,770
Particles have kinetic energy
and they have vector momentum.

471
00:32:42,770 --> 00:32:48,770
And you have been trained
painfully and completely

472
00:32:48,770 --> 00:32:52,160
in conservation of
energy and momentum,

473
00:32:52,160 --> 00:32:56,210
because it enables you to solve
all sorts of useful problems.

474
00:32:56,210 --> 00:33:02,800
So suppose the x-ray
comes in, hits the block.

475
00:33:02,800 --> 00:33:07,900
And so we have the
incident momentum

476
00:33:07,900 --> 00:33:10,464
and the x-ray is backscattered.

477
00:33:14,180 --> 00:33:22,890
And the scattering angle
theta is measured this way.

478
00:33:22,890 --> 00:33:29,210
So the difference in
momentum for this scattering

479
00:33:29,210 --> 00:33:35,760
is large for backscattering
and much less for forward

480
00:33:35,760 --> 00:33:36,748
scattering.

481
00:33:39,960 --> 00:33:43,865
Now, this momentum has to be
transferred to the electron.

482
00:33:47,890 --> 00:33:52,150
And so we can draw
conservation diagrams.

483
00:33:52,150 --> 00:33:55,220
Or for this case,
the backscattering.

484
00:33:55,220 --> 00:33:59,470
We have pn.

485
00:33:59,470 --> 00:34:05,000
We have the
electron, p electron.

486
00:34:05,000 --> 00:34:14,679
And we have the
momentum of the x-ray.

487
00:34:14,679 --> 00:34:21,500
OK, so this diagram
determines the momentum

488
00:34:21,500 --> 00:34:24,620
transferred to the electron.

489
00:34:24,620 --> 00:34:33,400
And if the x-ray photon
transfers energy to the--

490
00:34:33,400 --> 00:34:36,639
it transfers momentum
to the electron,

491
00:34:36,639 --> 00:34:39,040
it also transfers energy.

492
00:34:39,040 --> 00:34:40,929
So what we're going
to see-- and I'm just

493
00:34:40,929 --> 00:34:45,159
going to wave my hands, because
the mathematical analysis

494
00:34:45,159 --> 00:34:49,239
is something you can do, but
I don't want to go through it.

495
00:34:49,239 --> 00:34:53,239
I just want to show the
structure of the argument.

496
00:34:53,239 --> 00:34:58,940
What you measure
is the wavelength

497
00:34:58,940 --> 00:35:10,980
of the x-ray out minus the
wavelength of the x-ray in.

498
00:35:10,980 --> 00:35:16,190
And so if the x-ray
has transferred energy

499
00:35:16,190 --> 00:35:20,420
to the electron, it has
less energy when it leaves,

500
00:35:20,420 --> 00:35:22,200
and it has longer wavelength.

501
00:35:22,200 --> 00:35:27,350
So this is measurable, the
change in the wavelength

502
00:35:27,350 --> 00:35:30,840
of the x-ray, and
that's going to be--

503
00:35:30,840 --> 00:35:33,615
so we'll call that delta lambda.

504
00:35:33,615 --> 00:35:35,740
And that's going to be a
function of the scattering

505
00:35:35,740 --> 00:35:36,239
angle.

506
00:35:39,550 --> 00:35:44,450
So Compton scattering basically
says, OK, light is a particle.

507
00:35:44,450 --> 00:35:48,050
Particles have kinetic
energy and momentum.

508
00:35:48,050 --> 00:35:50,270
Conservation of
energy and momentum

509
00:35:50,270 --> 00:35:56,690
predicts a difference, a
redshift of the photon,

510
00:35:56,690 --> 00:36:00,190
which depends on the
scattering angle.

511
00:36:00,190 --> 00:36:02,410
The rest is all 8.01.

512
00:36:02,410 --> 00:36:03,980
You can do that.

513
00:36:03,980 --> 00:36:04,740
OK.

514
00:36:04,740 --> 00:36:17,250
And so what you end up finding
is that if the scattering is 0,

515
00:36:17,250 --> 00:36:20,050
then delta lambda is 0.

516
00:36:20,050 --> 00:36:22,300
There is no momentum.

517
00:36:22,300 --> 00:36:24,390
The photon just goes through.

518
00:36:24,390 --> 00:36:27,480
If the scattering is
pi, in other words,

519
00:36:27,480 --> 00:36:29,850
it's perfectly
backscattered, then

520
00:36:29,850 --> 00:36:32,550
delta lambda you
can calculate is

521
00:36:32,550 --> 00:36:39,450
2h over the mass of the electron
times the speed of light.

522
00:36:39,450 --> 00:36:41,780
Now, this quantity,
h over the mass

523
00:36:41,780 --> 00:36:46,260
of the electron times
the speed of light,

524
00:36:46,260 --> 00:36:48,150
has dimensions of length.

525
00:36:48,150 --> 00:36:55,600
And it's 0.02 or 3 angstroms.

526
00:36:55,600 --> 00:37:07,340
And this is called the Compton
wavelength of the electron.

527
00:37:07,340 --> 00:37:11,000
Because the photon is
scattering an electron.

528
00:37:11,000 --> 00:37:16,250
The change in wavelength of the
photon is determined by this.

529
00:37:16,250 --> 00:37:21,110
This is the momentum transfer.

530
00:37:21,110 --> 00:37:23,270
This gives you the
momentum transferred.

531
00:37:23,270 --> 00:37:26,510
And so this is a
universal constant.

532
00:37:26,510 --> 00:37:30,590
It says electrons
have, when they're

533
00:37:30,590 --> 00:37:35,570
scattered out of any
material, have this behavior.

534
00:37:35,570 --> 00:37:38,930
Again, universal and strange.

535
00:37:38,930 --> 00:37:42,410
The actual experiment,
since what you actually

536
00:37:42,410 --> 00:37:45,230
want to measure is the
change in lambda over lambda.

537
00:37:48,250 --> 00:37:52,680
The change in lambda doesn't
depend on lambda but this does.

538
00:37:52,680 --> 00:37:54,290
And so what you
want to do is make

539
00:37:54,290 --> 00:37:56,540
the observable thing large.

540
00:37:56,540 --> 00:37:59,360
And so you go to
a short wavelength

541
00:37:59,360 --> 00:38:02,320
to make this a large fractional
change that's easily measured.

542
00:38:05,120 --> 00:38:06,750
OK.

543
00:38:06,750 --> 00:38:09,280
The equations are derived
in the lecture notes

544
00:38:09,280 --> 00:38:11,290
and better in texts.

545
00:38:11,290 --> 00:38:14,830
And what I want to do
now is just tell you

546
00:38:14,830 --> 00:38:15,580
where we're going.

547
00:38:19,210 --> 00:38:23,860
We've talked about the wave
and particle nature of photons,

548
00:38:23,860 --> 00:38:25,840
of light.

549
00:38:25,840 --> 00:38:28,820
And the particle
nature is a surprise,

550
00:38:28,820 --> 00:38:34,900
but it's perfectly
understandable and observable.

551
00:38:34,900 --> 00:38:36,940
The next thing we want
to do is determine

552
00:38:36,940 --> 00:38:41,390
the wave nature of things
that we call particles.

553
00:38:41,390 --> 00:38:49,200
And so we're going to do other
kinds of simple scattering

554
00:38:49,200 --> 00:38:55,410
experiments where we discover
that the electron-- so we

555
00:38:55,410 --> 00:38:56,100
have some solid.

556
00:38:59,270 --> 00:39:06,030
And we have UV light or x-rays.

557
00:39:06,030 --> 00:39:08,190
And we go through this solid.

558
00:39:08,190 --> 00:39:12,620
And it's mostly transparent.

559
00:39:12,620 --> 00:39:13,655
It's mostly free space.

560
00:39:16,360 --> 00:39:21,900
And so this light is
interacting with the electrons.

561
00:39:21,900 --> 00:39:24,830
And maybe with the
other stuff that

562
00:39:24,830 --> 00:39:27,770
is involved in
matter, the nuclei.

563
00:39:27,770 --> 00:39:32,540
But the important thing
is that the electrons

564
00:39:32,540 --> 00:39:37,080
that get scattered are in
a kind of a diffuse state.

565
00:39:37,080 --> 00:39:39,700
This is mostly nothing.

566
00:39:39,700 --> 00:39:44,110
This material doesn't
scatter x-rays.

567
00:39:47,760 --> 00:39:50,550
It's mostly transparent.

568
00:39:50,550 --> 00:39:55,700
And so an explanation for that
is the Rutherford planetary

569
00:39:55,700 --> 00:39:58,940
model, where we have a
nucleus with a charge

570
00:39:58,940 --> 00:40:03,470
and electrons
orbiting that nucleus.

571
00:40:03,470 --> 00:40:05,300
And that's all very nice.

572
00:40:05,300 --> 00:40:10,120
It's a way of saying,
well, OK, the electrons

573
00:40:10,120 --> 00:40:14,870
are forced to choose
distances from the nucleus.

574
00:40:14,870 --> 00:40:18,259
And there's mostly empty space.

575
00:40:18,259 --> 00:40:20,300
But then you look more
closely, and the electrons

576
00:40:20,300 --> 00:40:21,230
are doing this.

577
00:40:21,230 --> 00:40:23,005
They're oscillating
in space, and they're

578
00:40:23,005 --> 00:40:24,005
going to radiate energy.

579
00:40:27,390 --> 00:40:28,980
And this radiation
of energy will

580
00:40:28,980 --> 00:40:31,020
cause the electrons to
spiral in and combine

581
00:40:31,020 --> 00:40:32,771
with the charge in the middle.

582
00:40:32,771 --> 00:40:33,645
And that's a problem.

583
00:40:36,510 --> 00:40:43,590
And so we have an explanation
for why matter is mostly

584
00:40:43,590 --> 00:40:47,000
empty space and a conundrum.

585
00:40:47,000 --> 00:40:51,940
The electron should
recombine with the nucleus.

586
00:40:51,940 --> 00:40:58,180
So how can matter be
relatively non-compressible?

587
00:40:58,180 --> 00:41:02,630
And the best explanation
is this planetary idea.

588
00:41:02,630 --> 00:41:04,695
But then we have this
thing we have to explain.

589
00:41:08,890 --> 00:41:12,220
Now, there's two
hypotheses for this, which

590
00:41:12,220 --> 00:41:15,230
are really just ad hoc things.

591
00:41:15,230 --> 00:41:22,480
One is the Bohr model where it
says, in order for the electron

592
00:41:22,480 --> 00:41:27,970
to obey some laws of physics
as it orbits the nucleus,

593
00:41:27,970 --> 00:41:30,390
it conserves angular momentum.

594
00:41:34,300 --> 00:41:39,150
Well, if it were rotating
combined with the nucleus,

595
00:41:39,150 --> 00:41:41,110
it wouldn't do that.

596
00:41:41,110 --> 00:41:43,320
And so that's sort of OK.

597
00:41:43,320 --> 00:41:49,500
And then there's de Broglie,
who was a very smart person.

598
00:41:49,500 --> 00:41:52,290
And he said that in
order for the electron

599
00:41:52,290 --> 00:41:56,010
not to annihilate itself as
it goes around the orbit,

600
00:41:56,010 --> 00:41:59,900
it has to have an integer
number of half wavelengths

601
00:41:59,900 --> 00:42:01,560
along that trajectory.

602
00:42:01,560 --> 00:42:03,710
Then it won't annihilate itself.

603
00:42:03,710 --> 00:42:06,690
And that is much better
than Bohr's hypothesis.

604
00:42:06,690 --> 00:42:08,970
But both of these
hypotheses lead

605
00:42:08,970 --> 00:42:12,240
to line spectra
hydrogen where you

606
00:42:12,240 --> 00:42:16,010
can build a really simple
model and you can predict

607
00:42:16,010 --> 00:42:18,720
to eight decimal places
all the absorption

608
00:42:18,720 --> 00:42:22,930
transitions of hydrogen atom.

609
00:42:22,930 --> 00:42:26,020
So a very simple model
leads to an incredibly

610
00:42:26,020 --> 00:42:29,550
powerful and mysterious result.

611
00:42:29,550 --> 00:42:33,650
There is another experiment that
I will talk about next lecture.

612
00:42:33,650 --> 00:42:36,790
And that is suppose we
have a thin sheet of metal.

613
00:42:39,570 --> 00:42:45,030
We have photons,
x-rays, or UV photons,

614
00:42:45,030 --> 00:42:47,455
impinging on this metal.

615
00:42:51,270 --> 00:42:53,490
There's diffraction
because there

616
00:42:53,490 --> 00:42:58,230
is regular distances
between the atoms

617
00:42:58,230 --> 00:43:01,470
in the particle in the foil.

618
00:43:01,470 --> 00:43:04,860
And so what we measure
is diffraction rings

619
00:43:04,860 --> 00:43:12,780
for the electron
and for the photon.

620
00:43:12,780 --> 00:43:19,500
And the diffraction
rings are identical when

621
00:43:19,500 --> 00:43:23,400
you choose the wavelength
of the particle

622
00:43:23,400 --> 00:43:27,830
to be equal to the
wavelength of the photon.

623
00:43:27,830 --> 00:43:31,520
And so this is another way of
showing wave particle duality.

624
00:43:31,520 --> 00:43:33,710
We can show that
they have wavelengths

625
00:43:33,710 --> 00:43:36,410
and we can calculate
to make them the same.

626
00:43:36,410 --> 00:43:38,450
So this is all very exciting.

627
00:43:38,450 --> 00:43:42,950
And this is about as much
philosophy and history

628
00:43:42,950 --> 00:43:46,170
as you're going to get from me.

629
00:43:46,170 --> 00:43:49,840
Once we understand that there
is something that we have to do,

630
00:43:49,840 --> 00:43:51,570
which is called
quantum mechanics,

631
00:43:51,570 --> 00:43:54,330
we're going to start
solving problems and then

632
00:43:54,330 --> 00:44:02,750
being able to understand
incredibly complicated effects

633
00:44:02,750 --> 00:44:05,320
beyond the simple problems.

634
00:44:05,320 --> 00:44:11,770
And that should be exciting, but
it should also be a little bit

635
00:44:11,770 --> 00:44:15,700
disturbing, because I will use
a technique called perturbation

636
00:44:15,700 --> 00:44:20,320
theory, which for some
reason all of the textbooks

637
00:44:20,320 --> 00:44:25,780
for a course at this level
either ignore or treat

638
00:44:25,780 --> 00:44:28,000
in the most superficial way.

639
00:44:28,000 --> 00:44:32,800
But perturbation theory is
a way of taking problems

640
00:44:32,800 --> 00:44:36,750
that we understand
and can solve exactly.

641
00:44:36,750 --> 00:44:41,690
And exactly means an infinite
number of states, all of which

642
00:44:41,690 --> 00:44:45,110
are given to us by
solving one equation.

643
00:44:45,110 --> 00:44:49,490
And we can then use them
to understand problems

644
00:44:49,490 --> 00:44:51,800
we can't solve exactly.

645
00:44:51,800 --> 00:44:54,680
And there'll be several ways
in which I deal with that.

646
00:44:54,680 --> 00:44:59,510
OK, so it's time to stop.

647
00:44:59,510 --> 00:45:04,730
And I hope you're excited about
what lies ahead, because it

648
00:45:04,730 --> 00:45:09,030
is strange and wonderful.

649
00:45:09,030 --> 00:45:13,530
And it says we can
look inside a molecule.

650
00:45:13,530 --> 00:45:14,940
We can make measurements.

651
00:45:14,940 --> 00:45:19,030
We can understand what this
molecule is going to do.

652
00:45:19,030 --> 00:45:22,760
But we have to develop
our new way of doing that.

653
00:45:22,760 --> 00:45:24,850
OK, thank you.