Why is there a maximum probability of finding an electron at an antinode in the de Broglie wave?

Question

And why is it that there is a 0 probability of finding an electron at the node of the de Broglie wave?

Thank-you.

Answer 1

Are you looking for a shallow or deep answer?

The shallow answer is that the probability goes as the square of the amplitude, so where the amplitude is zero (a node) the probability is zero, and where the amplitude is greatest the probability is greatest.

But the deep question is why should the wavefunction describe a probability at all? As far as I know no one has any idea at all.

Answer 2

The question answers itself. The probability of finding the electron at a point depends on the square of the wave function at that point. Maximum wave function (antinode) = greatest probability. Zero wavefunction (node) = zero probability.

Answer 3

I think you are talking about constructive and destructive interference. At the node, the wave patterns are destructive and the anti-node the opposite. Just like the way a string vibrates.

It you are looking for a different answer then it is just the way the probablity function maps out.