"What is a (spatial) frame of reference in quantum mechanics? When we make a transformation e.g. in a H-atom from the proton frame of reference to the electron frame of reference. The whole point of QM is that the electron cannot be treated as a dot somewhere in space but that it has an associated wavefunction and only acquires a certain position when I make an appropriate measurement. So how can I transform to the electron frame of reference making the origin to be the position of the electron if I don't know it?"

Mbalisikerc 2022-07-22 Answered
What is a (spatial) frame of reference in quantum mechanics?
When we make a transformation e.g. in a H-atom from the proton frame of reference to the electron frame of reference. The whole point of QM is that the electron cannot be treated as a dot somewhere in space but that it has an associated wavefunction and only acquires a certain position when I make an appropriate measurement. So how can I transform to the electron frame of reference making the origin to be the position of the electron if I don't know it?
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Answers (1)

eishale2n
Answered 2022-07-23 Author has 15 answers
The electron doesn't have a position so it makes no sense to talk about a frame with the origin at the position of the electron.
You can choose a frame in which the expectation value of the electron momentum is zero i.e. a frame in which the electron is on average stationary. Then shift the origin of this frame to make the expectation value of the electron position is zero. That would be a plausible candidate for the frame of the electron. This would of course coincide with the frame of the proton.
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