126.96.36.199 Solution hmolc-a
Suppose, given the wave function , that you found an electron near the left proton. What electron would it probably be? Suppose you found an electron at the point halfway in between the protons. What electron would that likely be?
The total probability of finding electron 1 at a position is
since is normalized. Similarly, the probability of finding electron 2 at position is .
If is close to the left proton, is significant, but is small, so you are much more likely to find electron 1 there than electron 2.
But at the point halfway in between the protons, and are equal by symmetry, and you are just as likely to find electron 1 there as electron 2.