The scattering states in one-dimensional Hermitian and non-Hermitian potentials are investigated. An analytical solution for the scattering states is presented in terms of Heun functions. It is shown that for some spe...The scattering states in one-dimensional Hermitian and non-Hermitian potentials are investigated. An analytical solution for the scattering states is presented in terms of Heun functions. It is shown that for some specially chosen parameter conditions, an infinite number of the exact scattering states is obtained. In the Hermitian potentials, they correspond to the reflectionless states. In the non-Hermitian complex potentials with parity-time symmetry, they are the unidirectionally reflectionless states.展开更多
We investigate a two-level quantum system driven by a Lorentzian-shaped pulse field.An analytical solution is presented in terms of the confluent Heun functions.It is shown that for specially chosen parameter conditio...We investigate a two-level quantum system driven by a Lorentzian-shaped pulse field.An analytical solution is presented in terms of the confluent Heun functions.It is shown that for specially chosen parameter conditions,there are a number of the exact analytical solutions in an explicit form.The dependence of the final transition probabilities in the two levels on the system parameters is derived analytically and confirmed numerically.展开更多
An analytical method is developed to study the two-mode quantum Rabi model.For certain specific parameter conditions,especially for the resonant conditions,we obtain an infinite number of the exact solutions of the ei...An analytical method is developed to study the two-mode quantum Rabi model.For certain specific parameter conditions,especially for the resonant conditions,we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies.It is shown that there exist new types of the exact energies which do not correspond to the level-crossings.Our analytical method may find applications in some related models.展开更多
基金Project supported by the Natural Science Foundation of Hainan Province,China(Grant No.2019RC179).
文摘The scattering states in one-dimensional Hermitian and non-Hermitian potentials are investigated. An analytical solution for the scattering states is presented in terms of Heun functions. It is shown that for some specially chosen parameter conditions, an infinite number of the exact scattering states is obtained. In the Hermitian potentials, they correspond to the reflectionless states. In the non-Hermitian complex potentials with parity-time symmetry, they are the unidirectionally reflectionless states.
基金Natural Science Foundation of Hainan Province,China(Grant No.2019RC179).
文摘We investigate a two-level quantum system driven by a Lorentzian-shaped pulse field.An analytical solution is presented in terms of the confluent Heun functions.It is shown that for specially chosen parameter conditions,there are a number of the exact analytical solutions in an explicit form.The dependence of the final transition probabilities in the two levels on the system parameters is derived analytically and confirmed numerically.
基金Supported by the National Natural Science Foundation of China under Grant No.11965011。
文摘An analytical method is developed to study the two-mode quantum Rabi model.For certain specific parameter conditions,especially for the resonant conditions,we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies.It is shown that there exist new types of the exact energies which do not correspond to the level-crossings.Our analytical method may find applications in some related models.
