[shamrock92]

Could someone explain to me how probability amplitude works with respect to electron clouds?

If we can calculate the probability of an electron being at any particular point, and there are an infinite number of possible points for the electron, then how can we attach a probability to each point such that the sum of all the probabilities is less than 1?

Fundamentally, I just don't get the concept of a wavefunction/probability amplitude.

[greg136]

Ok, imagine you have a single electron in a box. It must be somewhere in the box. So if you integrate the wavefunction for the electron over all space (normalizing the wavefunction), you must get 1. So in order to find a probability of an electron appearing between certain points, you just need to change your limits of integration.

The probability of an electron appearing at a certain point in space is zero (as you said, 1/an infinite number of positions).

The best we can do is to calculate the probability between two points in space.

[shamrock92]

Originally Posted by greg136

Ok, imagine you have a single electron in a box. It must be somewhere in the box. So if you integrate the wavefunction for the electron over all space (normalizing the wavefunction), you must get 1. So in order to find a probability of an electron appearing between certain points, you just need to change your limits of integration.

The probability of an electron appearing at a certain point in space is zero (as you said, 1/an infinite number of positions).

The best we can do is to calculate the probability between two points in space.

That makes a lot more sense.