PT Symmetry in Natanzon-class Potentials

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The conditions under which PT${\mathcal {PT}}$ 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 PT${\mathcal {PT}}$-parity properties of the y(x) function that is responsible for the transformation are studied in order to implement the PT${\mathcal {PT}}$ 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.

Original languageEnglish
Pages (from-to)2724-2736
Number of pages13
JournalInternational Journal of Theoretical Physics
Volume54
Issue number8
DOIs
Publication statusPublished - Aug 24 2015

Fingerprint

PT Symmetry
Parity
Variable Transformation
Jacobi Polynomials
parity
symmetry
Bound States
hypergeometric functions
Differential equation
Eigenvalue
differential equations
eigenvalues
Energy
Class
energy
Form

Keywords

  • Discrete energy eigenvalues
  • PT symmetry
  • Solvable potentials

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Mathematics(all)

Cite this

PT Symmetry in Natanzon-class Potentials. / Lévai, G.

In: International Journal of Theoretical Physics, Vol. 54, No. 8, 24.08.2015, p. 2724-2736.

Research output: Contribution to journalArticle

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