# 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 language English 2724-2736 13 International Journal of Theoretical Physics 54 8 https://doi.org/10.1007/s10773-014-2507-9 Published - 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

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

Research output: Contribution to journalArticle

title = "PT Symmetry in Natanzon-class Potentials",
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 Schr{\"o}dinger 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.",
keywords = "Discrete energy eigenvalues, PT symmetry, Solvable potentials",
author = "G. L{\'e}vai",
year = "2015",
month = "8",
day = "24",
doi = "10.1007/s10773-014-2507-9",
language = "English",
volume = "54",
pages = "2724--2736",
journal = "International Journal of Theoretical Physics",
issn = "0020-7748",
publisher = "Springer New York",
number = "8",

}

TY - JOUR

T1 - PT Symmetry in Natanzon-class Potentials

AU - Lévai, G.

PY - 2015/8/24

Y1 - 2015/8/24

N2 - 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.

AB - 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.

KW - Discrete energy eigenvalues

KW - PT symmetry

KW - Solvable potentials

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U2 - 10.1007/s10773-014-2507-9

DO - 10.1007/s10773-014-2507-9

M3 - Article

AN - SCOPUS:84937812553

VL - 54

SP - 2724

EP - 2736

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

SN - 0020-7748

IS - 8

ER -