Non-Relativistic Quantum Dynamics

Boon Leong Lan, Mehdi Pourzand, Rui Jian Chu

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.

Włodzimierz M. Tulczyjew

Boon Leong Lan, Rui Jian Chu

As an extension of our recent work (Results in Physics 12, 147-152 (2019)), we show, both theoretically and numerically, that the breakdown of agreement between the non-relativistic and relativistic quantum dynamical predictions in the non-relativistic regime also occurs for an electron subjected to a time-dependent force.

Boon Leong Lan, Rui Jian Chu

We show, both analytically and numerically, that the non-relativistic and relativistic quantum predictions for the dynamics of a prototypical driven electron – the periodically kicked rotor – do not always agree in the non-relativistic regime. The surprisingly different quantum predictions could be tested experimentally using ultra-cold fermionic atoms in a periodically-pulsed 1D optical lattice. Similar breakdown of agreement should occur for driven quantum systems in general. Since the relativistic theory should be empirically correct, it must be used instead of the approximate non-relativistic theory to correctly study the quantum dynamics of a driven system after the breakdown time, which could lead to important contributions in a wide range of fields from atomic to molecular, chemical and condensed-matter physics.

F. Coester