Hulthén势散射态的解析解

在任意l波的离心项1/r²用λ²e^-λr/(1-e^-λr)²近似表达的条件下，对Hulthén势的径向Schrdinger方程作自变量指数变换，使此转化为超几何微分方程，获得了Hulthén势s波散射态的精确解和非s波散射态的近似解析解.给出了相移的解析表达式和按“k/2π标度”归一化的用超几何函数表示的径向波函数.讨论了解析解的意义.

Analytical solution of scattering states for Hulthén potentials

In this paper, using the exponential function transformation, the radial Schrdinger equation with the Hulthén potential is transformed into a hypergeometricdifferential equation under the condition that an effective approximation as 1/r²≈λ²e^-λr/(1-e^-λr)² is used for the centrifugal term in the case of any l-states. The exact solution of s-wave scattering state and the approximate analytical solution of non-s-wave scattering states for the Schrdinger equation with the Hulthén potential are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale" and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.