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The PE is really arbitrary to within an additive constant - but no
additive constant can cancel out the *linear* term k*x1*x that arises
because of the translation, and that you need to fix your problem.
It's a pity that arbitrariness of PE is always discussed only with
reference to the gravitational PE near the Earth. There the PE is
linear, so when you translate the origin only a constant term arises,
which can be cancelled out by an additive constant.