I have a question concerning this image (Chemistry, Catherine E. Housecroft et al., Pearson Education, 2010).
In the text, it states the following:
"Each of the new molecular wavefunctions, $\Psi$(in-phase) and $\Psi$(out-of-phase), has an energy associated with it wich is dependent of the distance apart of the two hydrogen nuclei. As Figure 4.13 [provided image] shows, the energy of $\Psi$(in-phase) is always lower than $\Psi$(out-of-phase)."
The in-phase-function has a stabilized minimum, but the out-of-phase-function seems stable only at an infinite distance. For my intuition, the two graphs should be symmetric, since the two wavefunctions are alike and approach each other equally. Why do they behave like this?
Why are those functions not symmetric?
A following question would be, when I combine those two functions, I'll get a minimum at the x-value I marked with "minimum". Would this be the distance at which a nucleus in a stable diatomic molecule would be found like in this figure?
Thank you for your help and have a nice day :)