00:01
The heisenberg uncertainty principle arises because matter has a wave associated with it.
00:08
And let's see what the consequence of this principle is.
00:13
But the principle basically says that if there is uncertainty in the position of a particle, there will be uncertainty in the complementary quantity or variable, its momentum.
00:30
And the product of those two is greater than or equal to h bar over 2.
00:37
So one of the things is that there is a minimum uncertainty that comes from the product of those two.
00:46
As a consequence of this, a particle confined to a region will have a ground state energy.
00:53
It cannot sit with zero velocity, if you will.
01:01
If it has a fixed position, if you could shrink down the size of the region to almost nothing, the momentum will become extremely uncertain.
01:13
So there's kind of a trade -off here.
01:17
So here we're going to take as an example, an electron confined to maybe a crystal, but the width of the confined area in two dimensions.
01:34
Is going to mean that the momentum is going to have a minimum value.
01:42
Minimum momentum determined by the dimensions of the confinement.
01:55
Okay, so px minimum, for example, is going to be equal to h -bar over to delta x.
02:04
P -y minimum is going to be equal to h -bar over to delta -y.
02:12
And therefore we can say that the energy has at minimum, the kinetic energy, is px min squared over twice the mass of the electron, plus p .y min squared, twice the mass of the electron.
02:38
Okay, so we can actually figure this out if we know the dimensions of the confinement region, which are given.
02:49
1 .25 nanometers and 2 .76 nanometers.
02:56
So let me just write down some quantities that will work with.
03:01
H -bar...