薛定谔方程基态的修正迭代解
Revised Iterative Solution for Groundstate of Schroedinger Equation
摘要：
提出了一种基于格林函数的修正迭代法，求解Schroedinger方程的低阶量子波函数。特别地，得到了一个新的扰动能量表达式，它比传统的表达式简单得多。将该方法应用于求解非谐振子势。修正后的迭代过程给出了与基于单轨线求积法完全相同的结果。并以斯塔克效应为例，对修正迭代法与原迭代法进行了比较。经幂展开后，所得结果基本一致.
英文摘要：
A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schroedinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.
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