标题： 矩形势阱的精确格林函数及其在准束缚态中的应用 显示英文标题

标题： Exact Green's function for rectangular potentials and its application to quasi-bound states

摘要： 在本工作中，我们计算了任意矩形势场的精确格林函数。 具体来说，我们关注矩形量子阱的格林函数，扩展了对格林函数精确解的认识，并且综合和推广了文献中的结果。 精确公式的形式是路径之和，总是可以转化为闭合的解析表达式。 从格林函数的极点和留数中，得到了具有正确归一化常数的束缚态本征能量和本征函数。 为了展示该方法的通用性，本文还介绍了格林函数方法在矩形势垒中提取准束缚态信息的应用，此时标准的量子振幅分析会失效。 显示英文摘要

摘要： In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also generalizing and resuming results in the literature. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression. From the poles and residues of the Green's function the bound states eigenenergies and eigenfunctions with the correct normalization constant are obtained. In order to show the versatility of the method, an application of the Green's function approach to extract information of quasi-bound states in rectangular barriers, where the standard analysis of quantum amplitudes fail, is presented.