中文摘要：

利用B样条技术研究强磁场中GaAs量子环的能量和量子尺寸效应。计算结果表明：强磁场下（B〉3T）,量子环的基态能量E1和库仑能的绝对值EC随着磁场强度B的增大而增大。对应不同角动量（m=-1,-2,-3）,E1-B曲线的间距被放置在中心的正电荷的库仑场拉宽;基态能量E1随量子环半径r0的变化曲线出现一个极小值位置r00,r00随着B的增加而减小。在不同磁场下的E1-r0曲线的间距被放置在中心的正电荷的库仑场拉近,库仑能的绝对值EC随着r0的增大而线性减小;基态能量E1随着谐振子势ω0的增大而增大。库仑场使不同角动量（m=-1,-2,-3）下的E1-ω0曲线出现交叉现象,能级次序发生了变化。库仑能的绝对值EC随ω0的增加而非线性减小。

英文摘要：

The GaAs quantum ring energies and size-dependent effect are studied by B-spline technique in strong magnetic field.The calculated results show： In the strong magnetic field（B3T）,ground state energies E1 and absolute value of Coulomd energy ｜EC｜ increases with magnetic field strength B,and the distance between E1-B curves of different angular momentum（m=-1,-2,-3）are pulled apart by Coulomd field of positive charge placed in the center;As quantum ring radius r0 increase,every E1-r0 curve has a minimum position r00,which decreases as the magnetic field strength B increasing,and the distance between E1-r0 curves in different magnetic field strength B are pulled closely by Coulomd field of positive charge placed in the center;The absolute value of Coulomd energy ｜EC｜ decreases linearly as the magnetic field strength B increasing.The ground state energies E1 increase with harmonic potential ω0h,the E1-ω0h curves of different angular momentum（m=-1,-2,-3） cross each other under the impact of Coulomd field,which lead to a change of the energy levels in the order.The absolute value of Coulomd energy ｜EC｜ decreases nonlinearly as ω0h increasing.