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

In summary, the proton and electron in a hydrogen atom are described by separate wavefunctions, but when they come together, they form a joint wavefunction that describes the overall system. Some properties of the particles may be entangled, such as spin or total angular momentum. In quantum electrodynamics, the description of the hydrogen atom becomes more complex with contributions from states with higher particle numbers. However, in the non-relativistic theory, the wavefunction of the hydrogen atom can be factored into center-of-mass and relative motion parts, which are not a product state in terms of electron and proton observables.
  • #1
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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.
 
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  • #2
Stevexyz said:
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.
 
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  • #4
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.
 
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  • #5
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
 
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