A method is presented for transparent, energy-dependent boundary conditions for open, non-Hermitian systems, and is illustrated on an example of Stark resonances in a single-particle quantum system. The approach provides an alternative to external complex scaling, and is applicable when asymptotic solutions can be characterized at large distances from the origin. Its main benefit consists in a drastic reduction of the dimesnionality of the underlying eigenvalue problem. Besides application to quantum mechanics, the method can be used in other contexts such as in systems involving unstable optical cavities and lossy waveguides.

中文翻译：

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离散非厄米特特征值问题的透明边界条件

提出了一种用于开放非厄米系统的透明、能量相关边界条件的方法，并以单粒子量子系统中的斯塔克共振为例进行了说明。该方法提供了外部复杂缩放的替代方法，并且适用于可以在距原点很远的距离处表征渐近解的情况。它的主要好处在于大大减少了潜在特征值问题的维度。除了应用于量子力学之外，该方法还可用于其他环境，例如涉及不稳定光腔和有损波导的系统。