Superpotential for Novel Symmetry in Real and Complex Space

Abstract

We propose a new “superpotential” and find that neither the supersymmetric energy conditions nor the associated shape invariance conditions remain valid. On the other hand, a new energy condition En+−En(−)=2λ between the two partner Hamiltonians H(±) emerges. A mathematical proof supports the present findings, with examples being presented. It is observed that when the superpotential is associated with discontinuity or distortion, the SUSY energy conditions and the shape invariance conditions will no longer hold well. The above formalism is also valid in complex space for models involving PT-symmetry.

Keywords

• novel symmetry
• supersymmetry
• shape-invariance
• real and complex space
• invalidity