Isospectral partners for a complex PT-invariant potential

Details Isospectral partners for a complex PT-invariant potential Isospectral partners for a complex PT-invariant potential

2002-05-20

arxiv.org/abs/quant-ph/0205124v1

Physics

Quantum Physics

14 pages, 2 figures

Scientific paper

We construct isospectral partner potentials of a complex PT-invariant potential, viz., V(x) = V_1 sech ^2 x - i V_2 sech x tanh x using Darboux's method. Oneset of isospectral potentials are obatined which can be termed 'Satellite potentials', in the sense that they are pf the same form as the original potential. In a particular case, the supersymmetric partner potential has the same spectrum, including the zero energy ground state, a fact which cannot occur in conventional supersymmetric quantum mechanics with real potential. An explicit example of a non-trivial set of isospectral potential is also obtained.

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