An An exactly solvable PT symmetric potential from the Natanzon class

Abstract

The $\mathcal{P}\mathcal{T}$ symmetric version of the generalised Ginocchio potential, a member of the general exactly solvable Natanzon potential class is analysed and its properties are compared with those of $\mathcal{P}\mathcal{T}$ symmetric potentials from the more restricted shape-invariant class. It is found that the $\mathcal{P}\mathcal{T}$ symmetric generalised Ginocchio potential has a number of properties in common with the latter potentials: it can be generated by an imaginary coordinate shift $x\to x+\mathrm{i}\epsilon$; its states are characterised by the quasi-parity quantum number; the spontaneous breakdown of $\mathcal{P}\mathcal{T}$ symmetry occurs at the same time for all the energy levels; and it has two supersymmetric partners which cease to be $\mathcal{P}\mathcal{T}$ symmetric when the $\mathcal{P}\mathcal{T}$ symmetry of the original potential is spontaneously broken.

15 pages, 4 figures; to appear in J. Phys. A