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PROFESSOR: This is Louis--

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L-O-U-I-S d-e Broglie.

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And this is not
hyphenated nor together.

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They are separate.

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And the d is not
capitalized apparently too.

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And it's 1924, the photon
as a particle is clear,

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and the photon is also a wave.

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And Louis de Broglie
basically had a great insight

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in which he said that
if this is supposed

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to be a universal or a real
basic physical property

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that photons are
waves and particles,

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we knew them as waves and now
we know they're particles.

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But if they are dualed
with respect to each other,

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both descriptions are
in different regimes

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and in a sense, a particle
at the end of the day

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has wave attributes and
particle attributes.

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Wave attributes
because it interferes

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and is described by waves.

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And particle attributes is
because it has a definite

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amount of energy,
it comes in packets,

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they cannot be broken
into other things--

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this could be a more
general property.

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And in a sense, you could
say that de Broglie did

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a fundamental step almost
as important as Schrodinger

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when he claimed that all matter
particles behave as waves as

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well.

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Not just the photon, that's one
example, but everybody does.

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So associated to every modern
particle, there is a wave.

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But that is quite interesting
because in quantum mechanics,

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you have the photon
and it's a particle,

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but it's associated to a wave
and if you are a little quick,

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you say, oh sure, the
electromagnetic wave,

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but no, in quantum
mechanics, it's

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the probability amplitude
to be some work.

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Those are the numbers
we tracked in the mass

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and the interferometer, the
probability to be sampled.

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We didn't track the
waves or a single photon,

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the wave was a wave of
probability amplitude,

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something they didn't know at
all about yet at that time.

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So de Broglie's says just like
the photons have properties

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of particles and
properties of waves,

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every particle has
properties of waves as well

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and every wave has a
property of particles.

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But what is left unsaid here
is yes, you have a wave,

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but a wave of what?

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And we've already
told you a little bit,

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the answer has to do
with probability waves.

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So it's very strange that
the fundamental equation

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for a wave that represents
a particle is not

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an electric field or
a sound wave or this,

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it's for all of them
is a probability wave.

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Very, very surprising.

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But that's what de
Broglie's ideas led to.

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So if you had a photon, you
would say it's a particle,

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and when you think
of it as a particle,

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you would say it's a bundle of
some energy and some momentum.

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And if you think
of it as a wave,

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you would say it
has a frequency.

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And that's a particle wave
duality or in some sense,

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a particle wave
description of this

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object-- you have a particle
and a wave at the same time.

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When we have this, we have
a particle wave duality.

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And de Broglie said that this
is universal for all particles.

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Universal.

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And it appeared the
name of matter waves.

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These are the matter waves that
we're going to try to discuss.

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These are the waves
of something that

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are probability amplitudes
we're going to try to discuss.

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So you could say wave of what?

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What.

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And that comes
later, but the answer

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is probability amplitudes, those
complex numbers whose squares

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are probabilities.

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So just like we
had for a photon,

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de Broglie's idea was that we
would associate to a particle

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a wave that depends
on the momentum.

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So remember, the
Compton wavelength

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was a universal--
for any particle,

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the Compton wavelength
is just one number,

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but just for photons,
the wavelength depends

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on the momentum, so
in general, it should

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be dependent on the momentum.

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So we say that for a
particle of momentum p,

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we associate a wave--

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a plane wave, in fact--

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a plane wave, so we're getting
a little more technical,

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with of lambda equals
h over p, which

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is the de Broglie wavelength--

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de Broglie wavelength.

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So it's a pretty
daring statement.

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It was his PhD thesis and there
was no experimental evidence

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for it.

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It was a very
natural conjecture--

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we'll discuss it a lot
more next lecture--

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but there are very
little evidence for it.

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So experiments can
a few years later,

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and people saw that you
could interfere or diffract

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electrons.

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They would behave, colliding
into lattices like waves,

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and those are rather
famous experiments

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of Davisson and Germer.

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So particles, just like you
do as an interference effect--

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a two slit interference
effect in which

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you have a screen, a slit and
a screen, and you shine photons

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and then you get an
interference effect over here

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because of the wave
nature of photons,

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or in quantum
mechanics, you would

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say, because there are
probability amplitudes, that

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are complex numbers that
have to be interfered

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between the possibilities
of the two paths,

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because every photon
goes through both paths

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at the same time, these
experiments of interference,

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or two slit interference,
were done for electrons.

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And then, eventually,
they've been

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done for bigger and
bigger particles,

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so that it's not just
something that you do

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with elementary particles now.

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There's experiments done
about three years ago--

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I will put on the web site or on
the notes some of these things

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so that you can
see them, but now

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you can throw in
molecules here, molecules

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that have a weight of now 10,000
atomic mass units, like 10,000

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protons, like hundreds of--

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430 atom molecules, and you can
get an interference pattern,

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so it's pretty ridiculous.

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It's almost like, you one
day so you throw a baseball

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and you're going to see
an interference pattern,

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but, you know,
we've got to things

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with about 10,000 hydrogen
atoms and de Broglie

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wavelengths of 1 picometer,
which are pretty unbelievable.

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So the experiments are done
with those particles and in fact

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with electrons.

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People do those
experiments and they're

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in very beautiful
movies in which you

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see those electrons hitting
on the screen and then--

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I'll give you some links so
you can find them as well--

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and you see one
electron falls here

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and it gets detected and two
electrons, three electrons,

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four electrons, five electrons,
six electrons-- by the time

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you get 10,000 electrons,
you see lots of electrons

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here, very well here,
lots of electrons

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here, and the whole
interference pattern is created

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by sending one electron at
that time in an experiment that

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takes several hours
and it's reduced

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to a movie of about one minute.

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So particles, big particles
interfere, not just photons

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interfere.

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So those particles
have some waves,

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some matter waves discovered by
de Broglie, and next lecture,

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we're going to track
the story from de

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Broglie to the
Schrodinger equation

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where the nature of the
wave suddenly becomes clear.