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We show that the Calogero and Calogero-Sutherland models possess an N-bodygeneralization of shape invariance. We obtain the operator representation thatgives rise to this result, and discuss the implications of this result,including the possibility of solving these models using algebraic methods basedon this shape invariance. Our representation gives us a natural way toconstruct supersymmetric generalizations of these models, which are interestingboth in their own right and for the insights they offer in connection with theexact solubility of these models.Comment: Latex file, 23 pages, no picture

Shape invariance in the Calogero and Calogero-Sutherland models