圆柱形人造原子的能级结构及电子几率密度分布

Electron state structure and electron probability density distribution in an artificial atom of circular cylinder

通过求解定态薛定格方程得到了园柱形人造原子的能级结构，进而求出了电子几率密度分布。计算结果表明，电子被束缚在园柱内的条件与位阱深度Ｖ０及园柱的结构参数有关。当园柱的高ｈ＝４．００ｎｍ，半径ａ＝２．７５ｎｍ时，要求Ｖ０≥４．７４ｍｅＶ。在ｚ轴方向上的电子几率密度分布是以ｈ／２为对称中心周期震荡，并且柱体内外的电子几率密度的大小是可比较的；而在ｘｙ平面上的电子几率密度分布类似于氢原子，并且柱外的电子几率密度比柱内的要小得多。说明电子沿ｚ方向隧穿的几率较大，为两个甚至多个人造原子的ｚ方向耦联提供了理论依据。

The electron states and the electron probability densities are calculated by solving Schrdinger equation with three dimension potential well. The calculated results show that the condition of confining an electron in an artificial atom of circular cylinder depends on both the potential well deep and the size of the circular cylinder. For the circular cylinder of the radius a=2 75 nm and h =4 00 nm, it requires V 0≥ 4 74 meV to confine an electron. The electron probability density in z direction exhibits symmetrical and periodical oscillation as h/2 center, and the electron probability density outside the circular cylinder is comparable with that inside the circular cylinder. The electron probability density in x y plane is analogous to that of hydrogen atom, and the electron probability dencity outside the circularity is much smaller than that inside the circularity. It could be expected that the electron tunnel along z direction is possible.