  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 Schr\"odinger 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 Schr\"odinger equation, a free particle can have only PKE.
Starting from RQMEs and taking low momentum approximation, we derive NKE
Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger equation should be
employed. With the help of NKE Schr\"odinger 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
stablesystem, 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.
