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Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of \( \mathcal{P}\mathcal{T} \) symmetry

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Abstract

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. \( \mathcal{P}\mathcal{T} \) symmetry may facilitate reconciling our approach to the requirement that the rationally extended potentials be singularity free. Some examples are shown.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata, 700 009, India

    B. Bagchi

  2. Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050, Brussels, Belgium

    C. Quesne

  3. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700 035, India

    R. Roychoudhury

Authors
  1. B. Bagchi
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  2. C. Quesne
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  3. R. Roychoudhury
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Correspondence to B. Bagchi.

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Bagchi, B., Quesne, C. & Roychoudhury, R. Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of \( \mathcal{P}\mathcal{T} \) symmetry. Pramana - J Phys 73, 337–347 (2009). https://doi.org/10.1007/s12043-009-0126-4

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