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在轴对称径向Coulomb势场中单电子Schrding方程的解析解

Analytical solution of Schrding equation with radial coulomb potential in cylindrical coordinates
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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Schrding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. 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.
作者 朱俊廷 孟繁臣 周祚万
机构地区 西南交通大学材料科学与工程学院
出处 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第6期1280-1284,共5页 Journal of Sichuan University(Natural Science Edition)
基金 国家自然科学基金(51173148)
关键词 原子链 Schrding方程 柱坐标 解析解 atomic chain, Schroding equation, analytical solution, cylindrical Coordinate
分类号 O431 [机械工程—光学工程]
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参考文献10

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四川大学学报（自然科学版）
2012年 第6期

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