一种新的波函数匹配摄动法
New perturbation method with the matching of wave functions
摘要：
提出了一种新的方法来研究量子力学中束缚态的瑞利-薛定谔微扰展开。我们的灵感来自于具有多个（N个）不连续性的可解相互作用的巨大灵活性。在微扰区对标准匹配解进行了修正和迁移。我们利用局部波函数的整体重整化自由度，导出了一个紧凑的N维矩阵修正公式。在应用中，我们的配方显示非数值的任何分段常数零阶势的所有多项式扰动。
英文摘要：
We propose a new approach to the Rayleigh-Schrödinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piece-wise constant zero order potential.
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