Suppose you have a particle in one dimension in an energy eigenstate, i.e. Hψ(x)=Eψ(x) for some E. For an observer B in a coordinate frame with the origin translated some distance K to the right, the wavefunction of the particle looks like ψ'(x) = ψ(x+K).(adsbygoogle = window.adsbygoogle || []).push({});

Surely, we expect the energy that B measures to be the same as you measure, so Hψ'(x) = Eψ'(x) or in other words Hψ(x+K) = Eψ(x+K). But how can we prove this?

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# Invariance of energy under change of origin

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