I Are the proton and electron quantum entangled in the hydrogen atom?

[Stevexyz]

TL;DR

Do the proton and electron share the same wavefunction in describing the hydrogen atom?

The proton and electron are described by separate wavefunctions.
When they come together in the hydrogen atom are they quantum entangled and have a joint wavefunction.

 

[PeroK]

TL;DR Summary: Do the proton and electron share the same wavefunction in describing the hydrogen atom?

The proton and electron are described by separate wavefunctions.
When they come together in the hydrogen atom are they quantum entangled and have a joint wavefunction.

An electron and a proton are distinguishable particles and are described by different wavefunctions. That said, there is also a wavefunction for the overall system of the two particles. I.e. a wavefunction for the hydrogen atom, which will be a two-particle wavefunction.

Some of the properties of the two particles may be entangled, such as spin or total angular momentum.

 

[DrClaude]

Paolo Tommasini, Eddy Timmermans, A.F.R. de Toledo Piza,

The Hydrogen Atom as an Entangled Electron-Proton System​

https://arxiv.org/abs/quant-ph/9709052
https://doi.org/10.1119/1.18977

 

[LittleSchwinger]

Strictly speaking, since the overall hydrogen atom can be in a state which is entangled, the proton and electron won't individually have wave-functions but more general mixed states as mentioned in the paper linked in the previous post.

In QED the description of hydrogen becomes even more complex as there we have contributions from states with higher particle number beyond just the proton-electron pair.

 

[vanhees71]

The electron and proton in the H atom are entangled. In the non-relativistic (Schrödinger) theory you can argue as follows:

The wave function factorizes not in an electron and a proton part but in the "center-of mass" and "relative" motion part. In terms of electron and proton observables this is not a product state. For details, see the paper already quoted in #3:

https://arxiv.org/abs/quant-ph/9709052