In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u...In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u'(f)=f(t,u(t)) (t∈R), where f: R×R^+→Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.展开更多
The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector, is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in ...The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector, is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one- electron Sehrodinger equation. Analytical expressions for wave function and energy spectrum are obtained. It is shown that at small values of the stretch angle of spherical sector the problem is reduced to the conical QD problem. The comparison with previously performed works shows good agreement of results. As an application of the obtained results, the quantum transitions in the system are considered.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10271095), the Gansu Provincial Natural Science Foundation of China (No.ZS031-A25-003-Z) and the NWNU-KJCXGC-212 Foundation
文摘In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u'(f)=f(t,u(t)) (t∈R), where f: R×R^+→Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.
文摘The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector, is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one- electron Sehrodinger equation. Analytical expressions for wave function and energy spectrum are obtained. It is shown that at small values of the stretch angle of spherical sector the problem is reduced to the conical QD problem. The comparison with previously performed works shows good agreement of results. As an application of the obtained results, the quantum transitions in the system are considered.
