Category: Quantum Mechanics and Quantum Chemistry

Does the following thought experiment make sense?

Suppose we have a positively charged quantum mechanical particle in a finite potential energy well. Also suppose there is a free negatively charged quantum mechanical particle outside the potential energy well. There is a measurable probability that the positively charged particle will tunnel through the potential energy well and perhaps be attracted to the negatively charged particle. Likewise, the negatively charged particle has a finite probability of penetrating the potential energy well and hooking up with the positively charged particle should it still be trapped in the well. There is no “spooky action at a distance” to use Albert Einstein’s 1930s definition of quantum entanglement in this example since this electromagnetic attraction is a local phenomenon (?). The positively charged particle cannot exert an attractive force until it tunnels through the energy barrier or otherwise the negatively charged particle winds up breaking into the well. I don’t know exactly how quantum electrodynamics would explain this example. Perhaps the positively charged particle is a positron (antimatter lepton) and the negatively charged particle is a plain vanilla electron. We know that the local result of the interaction of our two matter-antimatter particles is an annihilation event whereby two energetic photons are created, or other products are generated.
https://en.wikipedia.org/wiki/Annihilation#/media/File:Electron_Positron_Annihilation.png