Hydrogenic entanglement

Abstract

Is there any entanglement in the simplest ubiquitous bound system? We study the solutions to the time-independent Schrödinger 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.