Phase-equivalent supersymmetric deep and shallow potentials

ABSTRACT PHASE-EQUIVALENT SUPERSYMMETRIC DEEP AND SHALLOW POTENTIALS ÖZER Okan M. Sc. in Physics Engineering Supervisor: Assoc. Prof. Dr Bülent GÖNÜL July 1999, 80 pages In this work we review theoretical formulation of the Supersymmetric Quantum Mechanics, which has received a lot of attention in the literature recently, and apply it to the determination of a shallow potential which is phase-equivalent to a deep potential, whose bound spectrum is identical except for the ground state which is suppressed. With this method, the non-physical Pauli forbidden bound states encountered in the spectrum of any potential can be eliminated, preserving the phase shift. The present approach is exact and provides differential relations between the wavefunctions of the two types of potentials. The method is applied to the a+a scattering, the deuteron and 11Be systems. We show that the deep potentials involving unphysical bound states and its supersymmetric, shallow, phase-equivalent partner excluding Pauli forbidden states give very similar physical quantities, although the corresponding eigenstates differ iiiin the node-number. This lends support to two nearly equivalent treatments of the Pauli principle. The supersymmetry aspect of nuclear interactions in the light of the calculation results obtained is discussed. Keywords : Supersymmetric Quantum Mechanics, Phase-Equivalent Potentials. IV