The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also app...The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also applied to obtain highly accurate energy eigenvalues. Additionally, the perturbation expansion, based on the AIM approach, is utilized to obtain simple analytic expressions for the energy eigenvalues.展开更多
A new example of PT-symmetric quasi-exactly solvable (QES) 22×-matrix Hamiltonian which is associated to a trigonometric Razhavi potential is con-sidered. Like the QES analytic method considered in the Ref. [1] [...A new example of PT-symmetric quasi-exactly solvable (QES) 22×-matrix Hamiltonian which is associated to a trigonometric Razhavi potential is con-sidered. Like the QES analytic method considered in the Ref. [1] [2], we es-tablish three necessary and sufficient algebraic conditions for this Hamilto-nian to have a finite-dimensional invariant vector space whose generic ele-ment is polynomial. This non hermitian matrix Hamiltonian is called qua-si-exactly solvable [3].展开更多
A class of quasi-exact solutions of the Rabi Hamiltonian,which describes a two-level atom interacting witha single-mode radiation field via a dipole interaction without the rotating-wave approximation,are obtained by ...A class of quasi-exact solutions of the Rabi Hamiltonian,which describes a two-level atom interacting witha single-mode radiation field via a dipole interaction without the rotating-wave approximation,are obtained by using awavefunction ansatz.Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and thefield frequency satisfy certain relations.As an example,the lowest exact energy level and the corresponding atom-fieldentanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings andcounter-rotating cases of the Rabi Hamiltonian.展开更多
In this paper quasi-exact solvability （QES） of Dirac equation with some scalar potentials based on s/（2） Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of t...In this paper quasi-exact solvability （QES） of Dirac equation with some scalar potentials based on s/（2） Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of the classes II, IV, V, and X potentials in the Turbiner＇s classification such that solved and the Bethe ansatz equations are derived in order to the Dirac equation with scalar potential is quasi-exactly obtain the energy eigenvalues and eigenfunctions.展开更多
Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact soluti...Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.展开更多
文摘The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also applied to obtain highly accurate energy eigenvalues. Additionally, the perturbation expansion, based on the AIM approach, is utilized to obtain simple analytic expressions for the energy eigenvalues.
文摘A new example of PT-symmetric quasi-exactly solvable (QES) 22×-matrix Hamiltonian which is associated to a trigonometric Razhavi potential is con-sidered. Like the QES analytic method considered in the Ref. [1] [2], we es-tablish three necessary and sufficient algebraic conditions for this Hamilto-nian to have a finite-dimensional invariant vector space whose generic ele-ment is polynomial. This non hermitian matrix Hamiltonian is called qua-si-exactly solvable [3].
基金the U.S. National Science Foundation under Grant Nos. 0140300 and 0500291the Southeastern Universities Research Association, the National Natural Science Foundation of China under Grant Nos. 10175031+1 种基金 10575047the LSU-LNNU Joint Research Program under Grant No. C164063
文摘A class of quasi-exact solutions of the Rabi Hamiltonian,which describes a two-level atom interacting witha single-mode radiation field via a dipole interaction without the rotating-wave approximation,are obtained by using awavefunction ansatz.Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and thefield frequency satisfy certain relations.As an example,the lowest exact energy level and the corresponding atom-fieldentanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings andcounter-rotating cases of the Rabi Hamiltonian.
文摘In this paper quasi-exact solvability （QES） of Dirac equation with some scalar potentials based on s/（2） Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of the classes II, IV, V, and X potentials in the Turbiner＇s classification such that solved and the Bethe ansatz equations are derived in order to the Dirac equation with scalar potential is quasi-exactly obtain the energy eigenvalues and eigenfunctions.
基金the financial support from the National Science Foundation of China(22078190 and 12002196)the National Key Research and Development Program of China(2020YFB1505802)。
文摘Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.
