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Staticization-based representations for Schr?dinger equations driven by Coulomb potentials

机译：库仑势驱动的薛定er方程的基于静态化表示

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摘要

A stochastic control representation for the Maslov dequantization of the solution of the Schr?dinger equation is obtained. The representation employs complex-valued diffusion process and stationarity of an action functional. The use of stationarity removes the need for convexity of the action, and hence there is no restriction on the duration of the problem. Previous efforts along this line were restricted to potentials which had holomorphic extensions to the entire space. The use of a stationarity based representation for the Coulomb potential removes that restriction. The result is a representation in terms of iterated staticization, which is expected to yield exceptional computational benefits.
机译：获得了薛定er方程解的Maslov反量化的随机控制表示。该表示采用复数值扩散过程和动作功能的平稳性。使用平稳性消除了动作凸出的需要，因此对问题的持续时间没有限制。沿这条线的先前努力仅限于对整个空间呈全同形扩展的潜力。库仑电位的基于平稳性的表示的使用消除了该限制。结果表示为迭代静态化，预计会产生出色的计算优势。

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