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847: FUNDAMENTALS OF PHYSICS II
Lecture 20 - Quantum Mechanics II [April 5, 2010]
Chapter 1: Review of Double Slit Experiment Using Electrons [00:00:00]
Professor Ramamurti Shankar: Well, this is just informal discussion till everybody's in here. So any
questions on the subject? What?
Student: Every question.
Professor Ramamurti Shankar: Everything. Okay, well, you know what, you guys should stop and
ask more things as you go along, because there is just no way you could get all of this. And it's a little
strange and only by talking about it, you will at least know what's going on. There's no way to make it
reasonable. It's not a reasonable world out there. I can only tell you what it is. I take that view; when I
teach quantum mechanics, just tell the rules and say, "This is what happens. This is how we calculate
things." And whether you like the formulas or not, it's not my concern. And the fact that it doesn't look
like daily life, also not my concern, because this is not daily life. Strange things happen. But you have to
keep me informed on how much you're following and what you are understanding, at any stage. Don't
wait for this to end, because it's not something where you can go on the last day and figure everything out.
And I will try to repeat at every stage what has gone up to that point, because the whole thing is only a few
lectures, maybe six or so. I can afford to go back every time to the beginning.
But I know that it makes sense to me, because I've seen it, and I don't know how it sounds to you. I have
no clue. You know that and so you have to speak up. You can ask any question you want, and I will try to
answer you, if it's within the realm of possibility.
Okay, so what have I said so far? So let me summarize. Even if you never came to last lecture, here is what
you should know about the last lecture, okay? Here's what I said. First thing I said is, everything is really
particles, all things, electrons, photons, protons, neutrons. They are all particles, so let there be no doubt
about that. By that, I mean if one of them hits your face, like an electron, you will feel it in only one tiny
region, one spot. Electron dumps all its charge, all its momentum, all its energy to one little part of your
face. So there's nothing wavelike about that. It's not like getting hit by a boxing glove, which can hit your
whole face. An electron hits one dot, or if it's an electron-detecting screen, only 1 pixel is hit by the
electron. And into that pixel is given all the charge, all the momentum, all the energy of that electron.
That's exactly what particles do. So when you encounter an electron, it is simply a particle. So where does
the problem come in? Where does the quantum mechanics come in? It comes in when you do the famous
double slit experiment. That's the key. The entire quantum mystery is in the double slit. Part of the
resolution is in the double slit, but the rest are a little more difficult, and I'll try to tell you. First I want to
tell you what goes wrong with Newtonian mechanics. After all, if everything is a particle, what's the big
deal, what's the problem? The double slit experiment is a problem. That's what puts the nail on the coffin
for Newtonian physics, and here it is in the basic version. You've got two slits.

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By the way, I'm going to call the particle the electron. They're all doing the same thing, so what applies to
one, applies to all of them. There is a source, like an electron gun, that emits electrons. In the old days,
televisions had the electron gun. And the gun emits the electrons, they go and hit the screen, they make a
little dot, and then the dot moves around, and you see your favorite show. Okay, this is the electron gun,
and the electron gun has been engineered to send electrons off a definite momentum. That you can get by
accelerating the electrons over a definite potential, and the gain of so many electron volts will turn into
kinetic energy. As for direction, if this gun is really far away to the left, in principle 1 mile, then the only
way electrons are going to go 1 mile and hit the screen is they're all basically moving in the horizontal
direction. Then you put a row of detectors in the back, which will detect electrons. Then this is slit 1 and
this is slit 2. You block slit 1.
In fact, let me say the following thing: what do we really know when we do the experiment? Once in a
while this gun will emit an electron, and we know it's emitted the electron, because it will recoil one way,
just like a gun, rifle. It will recoil. That's when we know the electron left. Then we don't know anything,
and suddenly, one of these guys says click. That means electron's arrived here. This is what we really
know. Everything else you say about the electron is conjecture at this point. You know it was here, you
know it was there. The question is, what was it doing in between? Now if you say, "Look, things cannot go
from here to there, except by following some path, I don't know what path it is." Maybe if it's an ordinary
particle, like a Newtonian particle, it will take some straight line, hit that slit, or go through that slit and
arrive here. So you might say, "I don't know the trajectory, but it's got to be some trajectory, maybe like
that, or maybe like that." So the electron takes some path and you can label the path as either through slit
1 or through slit 2.
Okay, now here is the problem. Suppose I do the experiment with slit 2 blocked, so you cannot even get
through this one, and I sit at a certain location for a certain amount of time, maybe 1 hour and I see how
many electrons come, and I get 5 electrons, with only 1 slit open. And if I move that observation point, I
get some pattern, pretty dull, looking like that, and I'm going to call it I
1
. That's the count, as a function of
position up and down that wall of detectors. Then I repeat the experiment with this guy closed and that
guy open, and I get another count, looks like that. Now I'm going to pick a location. These are not drawn
to scale or anything, so I'm not responsible for any of that. Maybe I'll at least show you one thing, which is
pretty important. This graph will be big in front of the second slit, which is somewhere here. It will look
like that. So I get I
1
when 1 is open and I get I
2
when 2 is open. This is I
1
, this is I
2
. Now I'm going to open
the two slits and I'm going to pick a particular location. It doesn't happen everywhere. I'm going to pick
one location called x. Where I used to get 5 electrons per hour with one thing open, and 5 electrons per
hour with the second thing open.
Now I want to open both and ask, what will I get? In Newtonian mechanics, there's only one possible
answer to that question, and that is 10, because we've got 5 this way and you've got 5 that way. And you
open both, whoever is going this way will keep going that way; whoever is going this way will keep going
this way. They will add up to give you 10. Now I told you, some people may say, "Well, maybe it's not 10,
because with both slits open, maybe someone from here can collide with someone from there. How do you
know that will not happen?" So I'm saying, do the experiment with such a feeble beam of electrons, there's

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847: FUNDAMENTALS OF PHYSICS II Lecture 20 - Quantum Mechanics II [April 5, 2010] Chapter 1: Review of Double Slit Experiment Using Electrons [00:00:00] Professor Ramamurti Shankar: Well, this is just informal discussion till everybody's in here. So any questions on the subject? What? Student: Every question. Professor Ramamurti Shankar: Everything. Okay, well, you know what, you guys should stop and ask more things as you go along, because there is just no way you could get all of this. And it's a little strange and only by talking about it, you will at least know what's going on. There's no way to make it reasonable. It's not a reasonable world out there. I can only tell you what it is. I take that view; when I teach quantum mechanics, just tell the rules and say, "This is what happens. This is how we calculate things." And whether you like the formulas or not, it's not my concern. And the fact that it doesn't look like daily life, also not my concern, because this is not daily life. Strange things happen. But you have to keep me informed on how much you're following and what you are understanding, at any stage. Don't wait for this to end, because it's not something where you can go on the last day and figure everything out. And I will try to repeat at every stage what has gone up to that point, because the whole thing is only a few lectures, maybe six or so. I can afford to go back every time to the beginning. But I know that it makes sense to me, because I've seen i ...
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