COMPLEXIFIED PSUSY AND SSUSY INTERPRETATIONS OF SOME PT-SYMMETRIC HAMILTONIANS POSSESSING TWO SERIES OF REAL ENERGY EIGENVALUES

Abstract

We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Pöschl–Teller and Scarf II, all of which reveal a double series of energy levels along with the corresponding superpotential. Inspired by the fact that two superpotentials reside naturally in order-two parasupersymmetry (PSUSY) and second-derivative supersymmetry (SSUSY) schemes, we complexify their frameworks to successfully account for the three potentials.