Groundbreaking discovery in quantum physics

To study the dynamics of quantum systems in the non-relativistic regime, the standard practice is to use non-relativistic quantum theory, instead of the more complicated relativistic version. This is because the former is conventionally thought to yield similar results to the latter.

Associate Professor Lan Boon Leong, together with two of his students, Mehdi Pourzand and Chu Rui Jian, proved that the conventional expectation is not true in general. Their findings were recently published in the journal ‘Results in Physics’.

The surprising conclusion in the paper is based on a key mathematical insight. The corresponding terms in the non-relativistic and relativistic equations for the time-dependent wave function (a fundamental quantity in quantum theory) differ by a phase factor, where the phase depends on the small difference between the non-relativistic and relativistic energies. However, because the phases grow with time, the agreement between the two wave functions will eventually break down.

The conclusion is also supported by numerical evidence for two systems – a model single-electron system and hydrogen atom – for which exact calculations could be performed using the two theories for comparison.

Numerical results showed that the agreement between the two theories can break down quickly, and the different predictions could be tested experimentally for hydrogen atom. The more encompassing relativistic theory should be empirically correct.

“Our finding implies that the relativistic theory must be used, instead of the non-relativistic theory, to correctly study quantum dynamics 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, which could lead to new understandings and discoveries,” said Lan, who is the Head of the Electrical and Computer Systems Engineering discipline.

“Our finding also suggests some of the numerous non-relativistic quantum dynamical studies to date are not entirely accurate. For example, the outstanding puzzling discrepancies between the non-relativistic quantum predictions and experimental measurements for the simplest chemical reaction (H + D2 → HD + D) might be resolved by using relativistic quantum theory,” he added.

To read the full paper, it can be accessed here: https://doi.org/10.1016/j.rinp.2018.11.050