Minimization of the Width as an Alternative to the Conventional Variation Method

The choice of param eters in a trial function to minimize the width Q2 (Q2 = 〈H2〉 − 〈H〉2 for a normalized wavefunction) is an alternative procedure to the usual minimization of 〈H〉 for generation of approximations to the true wavefunction. The minimization of the width is related to solving the eigenvalue equation by making the local energy HΦ/Φ as constant as possible, and other arguments can be put forth which suggest that this procedure should yield a wavefunction closer to the exact than that given by the usual variational method. For the ground state of H2 near its equilibrium internuclear distance, we choose the parameters ci in Φ = ΣiciΦi to (a) minimize the width and (b) minimize the energy. The expectation values from the function obtained by (a) are almost always worse than those from (b). Modifications of procedure (a) designed to improve the wavefunction in a specific region of configuration space were also attempted, without encouraging results.