Suppose we used a minus sign in our trial wave function (Equation 7.37) Without...

Suppose we used a minus sign in our trial wave function (Equation 7.37)

Without doing any new integrals, find F(x) (the analog to Equation 7.51) for this case, and construct the graph. Show that there is no evidence of bonding.13 (Since the variational principle only gives an upper bound, this doesn't prove that bonding cannot occur for such a state, but it certainly doesn't look promising). Comment: Actually, any function of the form

has the desired property that the electron is equally likely to be associated with either proton. However, since the Hamiltonian (Equation 7.35) is invariant under the interchange its eigenfunctions can be chosen to be 'simultaneously eigenfunctions of P. The plus sign (Equation 7.37) goes with the eigenvalue +1, and the minus sign (Equation 7.52) with the eigenvalue -1; nothing is to be gained by considering the ostensibly more general case (Equation 7.53), though you're welcome to try it, if you're interested.