Hi. It’s Mr. Andersen and this AP Physics essentials video 134. It is on the wave function.
Wave function can be used to calculate the probability of finding matter in one area
or another area. And so let’s start with a different kind of a wave, a crime wave.
This is a map of Washington DC and it shows where murders occurred from 2004-2006. So
you can see there are certain areas where we have more murders than other areas. Now
does it tell me where the next murder would occur? No. It just shows me where there is
a higher probability of it occurring. We use the same thing to describe where matter is.
So for example electrons, this does not show me where the electrons are, it just shows
me where there is more probability of finding those electrons. So matter can be treated
as a particle or a wave. As we get smaller and smaller and smaller remember we have to
shift to the wave model. Before we get to that let’s think of particles. A particle
in a box could be here or here or here, but if it is here it is not going to be anywhere
else in the box. But waves are different. We have to use a really complex wave function
to calculate the probability of finding that matter in one area or another. And so if this
is our box and we are using the wave model, we take the absolute value of the wave function
and we get something like this. This is going to show us the probability of finding the
location of matter in that one area. And so in AP Physics you have to be able to read
a wave equation or a wave rather function like this and figure out where is the probability
more likely. So before we get to that let’s start with a double slit experiment. Imagine
we have a wall right here. And it has two openings it, or two slits. And we are going
to fire paint balls through it. So as we shoot them through it they will hit on the screen.
And if we look at where they are distributed on the screen it would be somewhere like this.
That is because paint balls are like particles. Now if we were to cover up one of those then
we would only have the particles on the bottom side and likewise if we cover the bottom only
on the top side. But that is how particles behave. If we are doing waves it is different.
Let’s say these are water waves and we are able to measure where their amplitude is on
the other side. So they are going to interfere with themselves. And what we will get on the
other side are areas where we get huge waves and areas where they cancel each other out.
Waves are different than particles. Now let me kind of ask this question to you. What
would happen if we used electrons instead of paint balls? Well you might think they
look just like paint balls. So we are going to get that same distribution. What is interesting
is that you get interference. And so you get this wave property. And that indicates that
electrons are acting like waves. This makes sense. They are interfering with each other.
If we look at a screen in the back and let those electrons fire through, they will build
up, they will build up and you will get interference that looks like that. Now that is a little
crazy if you think about it. Because what they are doing is they are interfering. These
are the first electrons. The next electrons. The next electrons. Even though they are going
through one at a time they are actually interfering with electrons in the future or in the past.
That is kind of crazy. It gets crazier than that. If you look at one of these slits, and
so if you look here to see is the electron coming through this one or that one, something
puzzling happens. And what happens is they go back to acting like particles again. And
so the whole wave function is confounding to scientists. And we can not measure it.
If we actually look what happens, they quit acting like waves. And so how do you read
a wave function? Because that is what you have to do in this class. Well it will look
something like this. If this is a wave function of a particle, you could be asked are we more
likely to find the particle at x1 or x2. And the answer is really simple. We are going
to find it more likely at x2. Why is that? Because we have a greater amplitude of the
wave function here then we do over here. Or if we were to try this problem. So if we have
two wave function, A and B that represent two particles moving in the direction of x,
would we more likely find it at x0 on the left side, here or here? So what is the right
answer? How do you read this wave function? Well the right answer is going to be here,
at B. But why? Again it goes back to amplitude. So it is only going to be the amplitude. And
so do not worry about it is so compressed here. That does not tell you anything. What
you always want to do when you are looking at the wave function, find the highest amplitude,
that is going to be the highest probability. And so did you learn to use graphical wave
function to figure out qualitatively where that matter or that matter wave is going to be?
I hope so. And I hope that was helpful.