[Douglas]

Schrödinger's wave equation predicts the possible positions an electron can exist. However, when you square the equation, you end up with the probability of how likely it is to find an electron is a certain position.

a) Is what I have correct so far?

b) I am not making the connection on how this happens mathematically (squaring leading to probability).

Thanks for any help.

[Quantum07]

The wave equation in itself has NO physical meaning until the square of the equation is taken.

The square of the equation gives the probability of finding an electron at a certain distance from the nucleus. This is known as the Copenhagen interpretation of the wave equation. There are others but this interpretation has stood tests upon test upon test since it was first brought up.

When you use the operators for momentum, position, etc. and you take the squares of the wave function you end up with probabilities. The only thing the wave equation will give you once solved are the eigenvalues for the equation.

The schrodinger equation for the H atom can be solved EXACTLY and the solution will give you the energy levels for the H atom. It's much more complicated for multi-level electrons because you need to take into consideration electron electron repulsions.