00:02
We need to find the points of maximum and minimum probability density for the nth state of a particle in a 1d box.
00:10
And then we're going to check our result for the n equals 2 state.
00:18
So let's recall that the wave function for a one -dimensional box of length l, a psi of n is a sine of n pi x over l, where a is the normalization constant.
00:40
So then we know that the probability is equal to mod size squared.
00:49
So it is equal to a squared, sine squared, and pi x over l.
01:01
So the maximum value of the probability is 1.
01:07
So the argument of sign is what is driving this.
01:13
So we have that n pi x over l, it's a maximum when this is equal to pi over two, three pi over two, five pi over two, and so on...