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\({\mathcal {PT}}\) Symmetry in Natanzon-class Potentials

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Abstract

The conditions under which \({\mathcal {PT}}\) symmetry can be applied to the general six-parameter Natanzon potential class are investigated. For this the transformation of the differential equation of the Jacobi polynomials to the Schrödinger equation is considered in its most general form. The parity and \({\mathcal {PT}}\)-parity properties of the y(x) function that is responsible for the transformation are studied in order to implement the \({\mathcal {PT}}\) symmetry of the potential V(x). Situations in which the bound-state energy eigenvalues can or cannot become complex are identified. A number of known Natanzon-class potentials are analyzed. As a by-product, the relation of two variable transformation methods is clarified.

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Acknowledgments

This work was supported by the Hungarian Scientific Research Fund – OTKA, grant No. K112962.

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Authors and Affiliations

  1. Institute for Nuclear Research, Hungarian Academy of Sciences (Atomki), Pf. 51, 4001, Debrecen, Hungary

    Géza Lévai

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  1. Géza Lévai
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Correspondence to Géza Lévai.

Additional information

This work was supported by the Hungarian Scientific Research Fund – OTKA, grant No. K112962

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Lévai, G. \({\mathcal {PT}}\) Symmetry in Natanzon-class Potentials. Int J Theor Phys 54, 2724–2736 (2015). https://doi.org/10.1007/s10773-014-2507-9

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