IMPORTANCE OF PARAMETRIZING CONSTRAINTS IN QUANTUM-MECHANICAL VARIATIONAL CALCULATIONS

In variational calculations of quantum mechanics, constraints are sometimes imposed explicitly on the wave function. These constraints, which are deduced by physical arguments, are often not uniquely defined. In this work, we will point out the advantage of parametrizing constraints and letting the variational principle determine the best possible constraint for the problem. Examples are carried out to show the surprising effectiveness of the variational method if constraints are parametrized. It is also shown that misleading results may be obtained if a constraint is not parametrized.