On the combined effect of different symmetries on quantum mechanical potentials

摘要

We study the interrelation of PT symmetry, supersymmetry and Lie symmetries in the description of one-dimensional quantum mechanical potentials. Compared to their Hermitian counterparts, the complex PT potentials usually possess a second set of normalizable solutions, and the two sets can be distinguished by the quasi-parity quantum number q = ±1. We demonstrate that this doubling mechanism leads to larger potential algebras and also to the doubling of the SUSY partners of these potentials.