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
Stevexyz
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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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FAQ: Are the proton and electron quantum entangled in the hydrogen atom?

1. What does it mean for particles to be quantum entangled?

Quantum entanglement is a phenomenon where two or more particles become interconnected in such a way that the state of one particle cannot be described independently of the state of the other(s), even when the particles are separated by large distances. This means that measuring the state of one particle instantaneously affects the state of the other entangled particle(s).

2. Are protons and electrons in a hydrogen atom entangled?

In a hydrogen atom, the electron and the proton are not typically considered to be quantum entangled in the way that two particles can be in a dedicated entangled state. Instead, the electron occupies a quantum state around the proton, and while their states are correlated due to the electromagnetic interaction, this does not imply entanglement in the strictest sense.

3. How can we determine if two particles are entangled?

To determine if two particles are entangled, physicists can perform measurements on the particles and analyze the correlations between the results. If the measurement outcomes show statistical correlations that violate classical expectations, such as those predicted by Bell's theorem, the particles can be considered entangled.

4. Does the concept of entanglement apply to larger systems, like atoms or molecules?

Yes, the concept of entanglement applies to larger systems, including atoms and molecules. Many-body systems can exhibit entanglement between their constituent particles. However, the complexity increases, and entanglement can be more challenging to characterize and measure in larger systems compared to simpler two-particle systems.

5. What implications does entanglement have for quantum mechanics and technology?

Entanglement has profound implications for quantum mechanics, as it challenges classical intuitions about separability and locality. In technology, entanglement is a key resource for quantum computing, quantum cryptography, and quantum teleportation, enabling new capabilities that are not possible with classical systems.

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