二维和三维氢原子能级精细结构比较

Comparison of the Fine Structure of Energy Levels of a 2 - D and a 3 - D Hydrogen Atom

从二维和三维氢原子能级的精细结构表达式出发,进行数值计算,找到能级的精细结构数值的规律性。利用多媒体著作工具Multimedia TooBook计算能级并画出能级图和能级间距图,进行比较。证实从三维降为二维能级降低而能级间距增大。从基态到第一激发态、从第一激发态到第二激发态、从第二激发态到第三激发态二维能级间距分别是三维能级间距的4.74、2.05和1.61倍。

Based on the fine structure representations of energy levels of a 2-D and a 3-D hydrogen atom, this paper has calculated the numerical values of the energy levels and drawn the figures of energy levels and the difference of energy levels of 2-D and 3-D hydrogen atom with Multimedia ToolBook. By comparing energy levels of a 2-D hydrogen atom with those of a 3-D hydrogen, it is found that the decrease in energy levels was caused by reduction of dimensionality, and spacing between energy levels increased. The spacing of energy levels of a 2-D hydrogen atom from the ground state to the first exited state, the spacing of energy levels of a 2-D hydrogen atom from the first excited state to the second excited state and the spacing of energy levels of a 2-D hydrogen atom from the second excited state to the third excited state is 474, 205 and 161 times as that of a 3-D hydrogen atom.