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To study quantum dynamics in the non-relativistic regime, the standardpractice is to use non-relativistic quantum mechanics, instead of therelativistic theory, because it is thought the approximate non-relativisticresult is always close to the relativistic one. Here we present a theoreticalargument that this expectation is not true in general. In addition, supportingnumerical evidence for the free rotor and hydrogen atom also shows theagreement between the two theories can break down quickly. For the radialRydberg wave packet in hydrogen atom, the breakdown can occur beforespontaneous emission and thus could be tested experimentally. Our surprisingresult shows relativistic quantum mechanics must be used, instead of theapproximate non-relativistic theory, to correctly study quantum dynamics in thenon-relativistic regime after the breakdown time. This paradigm shift opens anew avenue of research in a wide range of fields from atomic to molecular,chemical and condensed-matter physics.

Breakdown of agreement between non-relativistic and relativistic quantum dynamical predictions in the non-relativistic regime