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

TL;DR

This paper challenges the common assumption that non-relativistic quantum mechanics always approximates relativistic predictions well in the non-relativistic regime, showing that the two can diverge significantly and that relativistic effects may be necessary for accurate quantum dynamics analysis.

Contribution

It provides a theoretical argument and numerical evidence demonstrating the breakdown of agreement between relativistic and non-relativistic quantum predictions in the non-relativistic regime, highlighting the need for relativistic quantum mechanics.

Findings

Agreement between theories can break down quickly for certain systems.

Breakdown can occur before spontaneous emission in hydrogen atom.

Relativistic quantum mechanics is necessary for accurate dynamics after breakdown.

Abstract

To study quantum dynamics in the non-relativistic regime, the standard practice is to use non-relativistic quantum mechanics, instead of the relativistic theory, because it is thought the approximate non-relativistic result is always close to the relativistic one. Here we present a theoretical argument that this expectation is not true in general. In addition, supporting numerical evidence for the free rotor and hydrogen atom also shows the agreement between the two theories can break down quickly. For the radial Rydberg wave packet in hydrogen atom, the breakdown can occur before spontaneous emission and thus could be tested experimentally. Our surprising result shows relativistic quantum mechanics must be used, instead of the approximate non-relativistic theory, to correctly study quantum dynamics in the non-relativistic regime after the breakdown time. This paradigm shift opens a new avenue of research in a wide range of fields from atomic to molecular, chemical and condensed-matter physics.