磁通量对二维谐振子的量子能级密度的影响(英文)  

Effect of a magnetic flux line on the quantum level density of a harmonic oscillator

作　　者：王德华[1] 李红艳[2] 马晓光[1] 王美山[1] 杨传路[1] 

机构地区：[1]鲁东大学物理与电子工程学院,烟台264025 [2]山东建筑大学理学院,济南250101

出　　处：《原子与分子物理学报》2007年第4期750-756,共7页Journal of Atomic and Molecular Physics

基　　金：国家自然科学基金(10604045);鲁东大学博士科研启动基金(202-23000301)

摘　　要：利用周期轨道理论,我们计算了在不同情况下,一个粒子在二维谐振子势中存在和不存在磁通量时的量子能级密度.重点讨论了磁通量对量子能级密度的影响.计算结果表明:当二维谐振子势的频率比值是有理数时,量子能级是分立的,能级密度中的每一条峰正好对应一个量子能级.然而,当频率比是无理数时,能级密度发生振荡,当加上磁通量后,振荡减小.这可以看作是Aharonov-Bohm效应的结果.Using the periodic orbit theory, we computed the quantum level density of a particle in the two-dimensional harmonic oscillator potential with and without the magnetic flux line for different cases. Especially discuss the influence of the magnetic flux line on the quantum level density. The results show when the frequency ratio of the two-dimensional harmonic potential is a rational number, the quantum level density is discrete. Each peak in the level density corresponds to one energy. However, when the frequency ratio is an irrational number, the level density is oscillating, when the magnetic flux is added, the amplitude of the oscilla- tion decreased. This can be considered as a consequence of Aharonov-Bohm effect.

关 键 词：周期轨道理论 量子能级密度 Aharonov—Bohm效应 

分 类 号：O56[理学—原子与分子物理]