New results by low momentum approximation from relativistic quantum mechanics equations and suggestion of experiments

Abstract

A fundamental belief is that the formulism of relativistic quantum mechanics equations (RQMEs) should remain in low momentum motion. However, it is found that some formulas from RQMEs were lost in Schrödinger equation. For example, a free relativistic particle has positive and negative energy branches. The former includes positive kinetic energy (PKE) and the latter negative kinetic energy (NKE). The latter should be treated on an equal footing as the former. Nevertheless, from Schrödinger equation, a free particle can have only PKE. Starting from RQMEs and taking low momentum approximation, we derive NKE Schrödinger equation which is for the cases that free particles have NKE. Thus negative energy branch of RQMEs can be retained in low momentum motion. We point out a fact that whether Schrödinger equation is applicable in a region where a particle’s energy E is less than potential V, E < V, has never been quantitatively verified. In such a region NKE Schrödinger equation should be employed. With the help of NKE Schrödinger equation, the lost formulas are recovered. The so-called difficulty of negative probability of Klein–Gordon equation for free particles is solved. A PKE (NKE) particle can have stationary motion only when it is subject to an attractive (repulsive) potential, which is determined by Virial theorem. Two NKE electrons in a potential can constitute a stable system, a new kind of possible mechanism for electron paring. The whole discussion stems from RQMEs with no any new postulation. Experiments are suggested, which may confirm that there are indeed NKE electrons.