本文研究了GaAs/Al $_{0.33}$ Ga $_{0.67}$ As量子阱中\textbf{tilted}磁场方向对二维氢原子能级和激子能级统计特性的影响。研究发现，随着磁场方向与原子平面法线方向夹角$α$的增大，量子混沌开始。QC的特征在于导致壳层结构消除的能级排斥和通过改变光谱统计性质。描述了波函数绝对值的平方随入射角$α$增大的空间分布的演化。在较宽的磁场强度范围内，计算得到了不同激发态的能量随倾斜角变化的差异。
英文摘要：
The aim of the current work is the research of the influence of the \textbf{tilted} magnetic field direction on statistical properties of energy levels of a two-dimensional (2D) hydrogen atom and of an exciton in GaAs/Al$_{0.33}$Ga$_{0.67}$As quantum well. It was discovered that the quantum chaos (QC) is initiated with an increasing angle $α$ between the magnetic field direction and the normal to the atomic plane. QC is characterized by the repulsion of levels leading to the eliminating of the shell structure and by changing the spectrum statistical properties. The evolution of the spatial distribution of the square of the absolute value of the wave function at an increasing angle $α$ was described. The differences of calculated dependencies of energies for various excited states on the tilt angle at a wide range of the magnetic field strength were obtained.
How Are Quantum Eigenfunctions of Hydrogen Atom Related To Its Classical Elliptic Orbits?
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Wilczek Quantum Center, Shanghai Institute for Advanced Studies（上海高等研究院吴文俊理论数学中心（斐泽克量子中心））；Hefei National Laboratory（合肥国家实验室）
