It is known that whenever the Hamiltonian contains an interaction part, the two interacting subsystems are entangled, thus an electron is surely entangled to a proton in a hydrogen atom. The discrepancy in mass of the two particles leads to a rather small entanglement, but it seems that no one has given a quantitative measure for it. [1] provides analysis on the reduced density function of the system, but gives no quantification; [2] measures entanglement in hyperfine interaction and the thermal entanglement with concurrence, but the entanglement in orbital motion is not defined. I have seen such entanglement quantified with von Neumann entropy for the internal motion of helium, where the atom is partitioned into two interacting electron-proton subsystems. So, is there a way to regard the electron and the proton as individual subsystems and quantify their orbital entanglement with one another?

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    $\begingroup$ You say 'no one has calculated this' like it would make a huge difference to the state of physics research if they did. It's a valid question, but if it's not in the published literature it's because it's ultimately of limited interest. $\endgroup$ – Emilio Pisanty Jul 15 '17 at 13:54
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    $\begingroup$ @EmilioPisanty: I know it's probably of limited utility value, as I've stated that the large difference in mass leads to small entanglement. I'm only curious, since by knowing, my sphere of knowledge would be a little bit more complete. $\endgroup$ – updraft Jul 15 '17 at 14:14

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