Is there any entanglement in the simplest ubiquitous bound system? We study the solutions to the time-independent Schr\"odinger equation for a Hydrogenic system and devise two entanglement tests for free and localised states. For free Hydrogenic systems, we compute the Schmidt basis diagonalisation for general energy eigenstates, and for a Hydrogenic system localised to a three-dimensional Gaussian wavepacket, we demonstrate that measuring its second moments is sufficient for detecting entanglement. Our results apply to any system that exhibits Hydrogenic structure.

中文翻译：

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氢纠缠

最简单的泛在束缚系统中是否有任何纠缠？我们研究了氢系统的与时间无关的 Schr\"odinger 方程的解，并为自由和局域状态设计了两个纠缠测试。对于自由氢系统，我们计算一般能量本征态的施密特基对角化，以及氢系统的施密特基对角化定位到三维高斯波包，我们证明测量其二阶矩足以检测纠缠。我们的结果适用于任何表现出氢结构的系统。