$\cal{PT}$ symmetric models with nonlinear pseudo supersymmetry

Details $\cal{PT}$ symmetric models with nonlinear pseudo supersymmetry $\cal{PT}$ symmetric models with nonlinear pseudo supersymmetry

2005-05-30

arxiv.org/abs/quant-ph/0505221v1

J. Math. Phys. 46, 032102 - 032118 (2005)

Physics

Quantum Physics

18 pages

Scientific paper

10.1063/1.1843273

By applying the higher order Darboux algorithm to an exactly solvable non Hermitian ${\cal{PT}}$ symmetric potential, we obtain a hierarchy of new exactly solvable non Hermitian ${\cal{PT}}$ symmetric potentials with real spectra. It is shown that the symmetry underlying the potentials so generated and the original one is {\it nonlinear pseudo supersymmetry}. We also show that this formalism can be used to generate a larger class of new solvable potentials when applied to non Hermitian systems.

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