Introduction to Quantum Mechanics · Problem 8.10

The Variational Principle — David J. Griffiths

Physics — Quantum Mechanics · antibonding_orbital

Problem

Suppose we used a *minus* sign in our trial wave function (Equation 8.38):

\psi = A\left[\psi_0(r) - \psi_0\left(r'\right)\right]. \tag{8.53}

Without doing any new integrals, find

F(x)

(the analog to Equation 8.52) for this case, and construct the graph. Show that there is no evidence of bonding. (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.)

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