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由于量子环特殊的结构,我们尝试过不少方法,发现一般传统方法很难求解薛定谔方程,故很难求出它的波函数和能级。国内外很多学者从事这方面的研究,但发表的文献非常少。有必要寻找一些新的方法从事这方面的研究工作,本文中采用了B样条函数近似拟合波函数的方法,计算了一个在谐振子束缚势和磁场作用下含有杂质的二维量子环中的电子能级。研究了电子能级随磁场强度、束缚势的变化关系以及电子能级与量子环半径的关系。我们发现电子能级随磁场强度、束缚势强度的增强而增强;每一个能级都有一个最小值在特定的量子环半径上,并且随着能级的增加,最小值的位置向半径大的方向偏移。
Due to the special structure of the quantum ring, we have tried many methods and found that it is very difficult to solve the Schrödinger equation by the traditional method, so it is difficult to find its wave function and energy level. Many scholars at home and abroad engaged in this research, but published a very small amount of literature. It is necessary to find some new methods to do this research work. In this paper, a method of approximating the wave function by the B-spline function is adopted, and a two-dimensional quantum ring containing impurities under the binding of the harmonic oscillator and the magnetic field Electronic level. The relationship between the electron level and the magnetic field strength and the binding energy and the relationship between the electron energy level and the radius of the quantum ring were studied. We find that the electron level increases with the increase of magnetic field strength and bond strength. Each energy level has a minimum value at a specific quantum ring radius, and as the energy level increases, Offset.