••• Consider the wave functions ψ± discussed in Section 12.4. In that discussion we did n...

••• Consider the wave functions ψ± discussed in Section 12.4. In that discussion we did not worry about normalization, but ψ± should strictly have been defined as ψ+ = B(ψ1 + ψ2) and ψ− = C(ψ1 − ψ2), where B and C are normalization constants needed to ensure that ∫ |ψ|2 dV =1. (a) If ψ1 and ψ2 do not overlap (or, more precisely, if their overlap is negligible), show that . (Assume that ψ1 and ψ2 are themselves normalized.) (b) If ψ1 and ψ2 overlap a little, argue that B is a little less than and hence that at the midpoint between the two protons, |ψ+|2 is just a little less than 2|ψ1|2. This proves our claim that ψ+ concentrates the probability density between the two protons. (c) Argue similarly that C must be a little larger than .