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

作者：Xie, Qiongtao^*; Yan, Lina; Wang, Linmao; Fu, Jun

来源：Pramana - Journal of Physics, 2016, 86(5): 965-972.

DOI：10.1007/s12043-015-1139-9

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

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.

• 出版日期2016-5
• 单位海南师范大学