Abstract
The validity of the results of finite basis, constrained variational calculations with unbounded operators has remained unquestioned despite the mathematical difficulties in an infinite basis pointed out by Fonte and Schiffrer. It will be shown here that the difficulties associated with unbounded operators are not restricted to infinite bases and that, in fact, the consequences are equally severe in finite bases. The demonstration will be made both for a one dimensional, one body model and in a full three dimensional, many body calculation typical of those currently being employed in nuclear physics. The correct procedure for imposing such constraints, e.g., the quadrupole constraint, and the validity of previous calculations remain open questions.
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