00:01
Okay, we have a wave function that's describing some particle, and we have three regions, x between 0 and a, and x between a and w, and we want to match up boundary conditions and figure out what some of these constants are.
00:29
So at x equals a, psi 1 of a has to be psi 2 of a.
00:35
So we just plug a into both of these for x.
00:40
We get this equation.
00:53
And then we do the same thing for the derivatives.
00:55
We take the derivative because the derivatives have to match as well at a.
01:00
So we take the two derivatives and set them equal.
01:12
And it gives us this equation.
01:18
And don't forget the c up here.
01:22
So we have two equations, that one and this one.
01:27
Okay.
01:30
And we can solve them for c and d in terms of a and b.
01:41
So let's number them one and two.
01:44
Then equation two tells us that a minus d is minus a b.
01:53
And then we plug that into one.
01:56
And we get a, b squared plus quantity squared plus b for c.
02:10
And then we can plug back into.
02:13
Equation two or just solve it and find out that d is equal to a plus ab and that works out just fine then we want to know what's going on at x we want to find out what w is which is that upper limit is where psi 2 and psi 3 meet and si 3 is zero so x minus d quantity squared minus c has to be zero.
03:10
And so we substituted in our values for c and d.
03:15
First of all, we found out that c is w minus d squared...
