辅助场方法与指数势薛定谔方程的解析解
Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials
摘要：
辅助场方法是计算薛定谔方程近似解析本征能和本征向量的一种新的有效方法。这种方法已成功地应用于幂律和对数形式的中心势的情况。在目前的工作中，我们表明，薛定谔方程的指数势的形式$-αr^λ\exp(-βr)$也可以解析求解使用辅助场方法。给出了这些势的临界高度和能级的计算公式。特别注意的汤川潜力和纯指数。
英文摘要：
The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies and eigenvectors of the Schrödinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schrödinger equation with exponential potentials of the form $-αr^λ\exp(-βr)$ can also be analytically solved by using the auxiliary field method. Formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn on the Yukawa potential and the pure exponential one.
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