VARIATIONAL CALCULATIONS WITH UNBOUNDED OPERATORS
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In a constrained variational calculation, the minimum of the expectation value of an operator H, subject to the constraint that the expectation value of an operator A have a definite value, is sought. Fonte and Schiffrer have recently noted that the Lagrange multiplier method of of determining the solution to this problem fails when the operator A is unbounded. We show that in this case, the expectation value of H can be made arbitrarily close to the unconstrained minimum, for any constrained value of A. This result casts doubt on the validity of the results of calculations, in which an unbounded operator (such as the quadrupole moment of a nucleus) is constrained, even if these calculations are carried out using a finite-dimensional basis in which the restricted operator is bounded. Various alternatives to these calculations are discussed. 1976.