The behaviors of the wave functions of small molecules with negative kinetic energies

Abstract

According to relativistic quantum mechanics, particles can be of negative kinetic energies (NKE). The author asserts in his previous works that the NKE substances are dark matters. Some NKE particles, say a pair of NKE electrons, can constitute a stable system by means of the repulsive interaction between them. In the present work, two simplest three-particle systems are investigated. One consists of two NKE positrons and one NKE proton, called dark hydrogen anion. The other is composed of two NKE protons and one NKE positron, called dark hydrogen molecule cation. They are so named because the Hamiltonians of them can correspond to those of the hydrogen anion and hydrogen molecule cation. In evaluating the dark hydrogen molecule cation, the famous Born-Oppenheimer approximation does not apply, i.e., the NKE of the protons cannot be neglected. Without the NKE, the system cannot be stable. Our study reveals that in a NKE system, the particles with the same kind of electric charge combine tightly. This is to enhance the repulsive Coulomb potential so as to raise the total energy as far as possible. A great amount of NKE particles can compose a dense and dark macroscopic NKE body. Thus, it is conjectured that some remote dark celestial bodies may be NKE ones other than the well-known black holes. The discrepancies between the black holes and macroscopic NKE bodies are pointed out.