Problems of angular momentum projection in nuclear physics

In nuclear models approximate wave functions are often used which do no have sharp angular momentum as required of the exact wave functions. It seem obvious that model wave functions of this type should be improved by projection onto states of good angular momentum. It is not the purpose of this paper to discuss the technical difficulties of projection (which can be formidable for many particle systems), but rather to present in an elementary way certain fundamental ambiguities in the use of projection. An application to high spin states near the yrast line is suggested.