中文摘要：

基于一维原子链对电子的约束势场具有径向对称特点，求解了轴对称径向Coulomb势场中单电子Schr6ding的本征值和本征函数问题．解析求解在柱坐标下通过分离变量法进行，分别获得轴向、角向和径向本征方程的严格解，其中径向方程经变量代换后化为Bessel方程形式．文中分析了电子的能级结构和简并情况，并与类氢原子体系进行对照讨论．本文结果对揭示一维原子链体系（特别是激发态）的光量子性质和电子输运性质具有一定参考意义．

英文摘要：

The behavior of electron constrained in the radial Coulomb potential similar to the situation of atomic chain was studied theoretically. The analytical solution of Schroding equation in cylindrical coor- dinates （r, θ, z） was given, and the electronic energy levels and wave functions were obtained. It shows that Schr6ding equation in cylindrical coordinates can he simplified to three ordinary differential equa- tions with exact analytic solutions. The electronic energy structure and degree of degeneracy was dis- cussed, comparing with that of the hydrogen-like atom. The present results are meaningful when the photoelectric properties and the electrical transport properties are investigated for one-dimensional atom- ic chain especially in its excited states.