Abstract
We show that the removal of Pauli forbidden s-states in the local α-α potential of Buck et al., by means of successive supersymmetric transformations, leads to a simultaneous removal of groups of “unphysical” states of the 3 α- and 4 α-systems, but that the remaining states are largely unaffected. Potentials of different strength but similar shape have the same property of spectrum conservation. Counter examples show that it is not valid for all types of potential however. Its main significance lies in the extension of nonrelativistic supersymmetric quantum mechanics form two to many bodies.
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