00:01
Show that the wave function is an eigenfunction of the momentum operator.
00:06
So this eigenvalue equation will look like this.
00:11
So we have the momentum operator, p, acting on the wave function.
00:18
And this will be equal to some scalar times the wave function.
00:27
The momentum operator is equal to negative i, h bar times the first derivative with respect to x so we can take that and act it on our wave function here so it becomes negative i h bar times the derivative of our wave function here so we're going to differentiation here.
01:13
So we'll leave this negative i h bar out in the front.
01:17
And when we take the derivative of cosine 4x, we get 4 times the cosine of 4x, or rather differentiate there fully, negative 4 sine of 4x.
01:34
And that's just by the chain rule...