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An update on the PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally extended supersymmetric partners

par Bagchi, Bijan;Quesne, Christiane
Référence Journal of Physics A: Mathematical and Theoretical, 43, 30, 305301
Publication Publié, 2010

Article révisé par les pairs

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Résumé :

The PT-symmetric complexi?ed Scarf II potential V(x) =-V 1sech2 x + iV2sechx tanh x, V1 > 0, V2 ≠= 0, is revisited to study the interplay among its coupling parameters. The existence of an isolated real and positive energy level that has recently been identfied as a spectral singularity or zero-width resonance is here demonstrated through the behaviour of the corresponding wavefunctions and some property of the associated pseudo-norms is pointed out. We also construct four different rationally extended supersymmetric partners to V(x), which are PT-symmetric or complex non-PT-symmetric according to the coupling parameters range. A detailed study of one of these partners reveals that SUSY preserves the V(x) spectral singularity existence. © 2010 IOP Publishing Ltd.