An exactly solvable PT symmetric potential from the Natanzon class

Details An exactly solvable PT symmetric potential from the Natanzon class An exactly solvable PT symmetric potential from the Natanzon class

2003-06-04

arxiv.org/abs/quant-ph/0306031v1

J. Phys. A: Math. Gen. 36 (2003) 7611

Physics

Quantum Physics

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

Scientific paper

10.1088/0305-4470/36/27/313

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

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