The resultant \(\psi\) plot is the result of both negative and positive \(\psi\) values. It seem that at this level, as a mathematical sum, \(\psi\) is allow to be negative, however after the summation, the boundary condition, \(\psi\ne0\) is applied and the resultant \(\psi\) is positive above the \(\psi=0\) line.
What determines \(A\) during the interaction of \(\psi\)s? When \(A=0\), the corresponding \(\psi\) graph is,
The resultant \(\psi_{p1}+\psi_{p2}\lt0\). If
\(F=-\psi\)
is an attractive force,
\(F=-(-\psi)=+\psi\)
will be a repulsive force.
\(\psi\)s in close proximity, when they overlap, is attractive. They move relative to one another but remains overlapped. When they do not overlap they are repulsive.
But this result comes from considering negative \(\psi\) at a theoretical level. When \(\psi\) sum to negative, they simply do not sum at all.
Theoretically negative \(\psi\) exist. And valid conclusions can be drawn from \(-\psi\). We are analyzing particles in general not differentiated into protons, electrons, etc. Protons in close proximity, when their \(\psi\)s overlap will stick together, too.
