, Volume 86, Issue 5, pp 965–972 | Cite as

Analytical results for non-Hermitian parity–time-symmetric and Hermitian asymmetric volcano potentials

  • JUN FU


We investigate both the non-Hermitian parity–time-(PT-)symmetric and Hermitian asymmetric volcano potentials, and present the analytical solution in terms of the confluent Heun function. Under certain special conditions, the confluent Heun function can be terminated as a polynomial, thereby leading to certain exact analytical results. It is found that the non-Hermitian PT-symmetric volcano potentials support the normalizable and non-normalizable reflectionless states with real energies. The Hermitian asymmetric volcano potentials allow normalizable reflectionless states with complex energies.


Volcano potentials Heun confluent equation Heun confluent function reflectionless scattering state. 


03.65.Ge 03.65.Fd 11.30.Er 



This work was supported by the National Natural Science Foundation of China under Grant No. 11375059 and the Scientific Research Fund of Hunan Provincial Education Department under Grant No. 13A058.


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Copyright information

© Indian Academy of Sciences 2016

Authors and Affiliations

  1. 1.College of Physics and Electronic EngineeringHainan Normal UniversityHaikouChina

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