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Assuming the many-worlds interpretation of quantum mechanics is correct.

Using a toy problem of a Universe with only one hydrogen atom, with the electron starting near the proton.

Would the following description of the situation be accurate?

The probability density distribution of the electron around the atomic nucleus would expand at the speed of light in all directions, although most of the probability density distribution of the electron would remain very close to the proton.

Therefore, at any given moment and position in the future light cone of the proton there would be at least one Everett branch where the electron would be at that position.

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MWI doesn't necessarily involve any branching. The most austere versions of MWI don't. They simply consist of stating that we have a Hilbert space and unitary evolution.

In versions of MWI where people talk about branching, they're basically approximating decoherence. Decoherence involves the interaction of a particle with the environment. In your universe with only one atom, there is no such interaction.

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  • $\begingroup$ Thanks a lot. Does unitary evolution mean the electron will remain in only one location? What if instead, it was an electron going through a slit? (and the rest of the Universe was empty) Given I already have a decent math background, where could I learn the math behind this? $\endgroup$ – Mati Roy Mar 22 at 20:47

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