Abstract

The Schrödinger equation with a Gaussian potential to model a confined system as a quantum dot or a hydrogen atom inside a fullerene is solved by using the analytic continuation method. The use of the Rodrigues formula allows us to obtain in an easy way the coefficients of the power series expansion of the Gaussian potential in terms of the Hermite polynomials. Recurrence formulas have been obtained for the series of the states of one electron confined by that potential. This method is simpler and computationally more efficient than others employed to model quantum dots using Gaussian potentials.

Graphic Abstract

中文翻译：

---

解析连续法计算富勒烯中的受限轨道和量子点

摘要

通过使用解析连续方法，求解了具有高斯势的薛定to方程，用于将受限系统建模为富勒烯内部的量子点或氢原子。Rodrigues公式的使用使我们能够轻松地获得根据Hermite多项式计算的高斯势的幂级数展开系数。已为受该电势限制的一个电子的一系列状态获得了递推公式。与使用高斯势来建模量子点的其他方法相比，该方法更简单且计算效率更高。

图形摘要