Negative Kinetic Energy Supersymmetric Quantum Mechanics

M. Kibler, Mohammed Daoud

Lu Huan, Wan Buyong, Liu Yao +1 more

The issues of the negative energy and the negative kinetic energy remain among the most profound and actively debated topics in physics. Based on the negative-kinetic-energy supersymmetric quantum mechanics (NKE-SUSYQM), this paper explores the supersymmetric algebra in depth. First, we begin with a concise overview of how the negative-kinetic-energy Schrödinger equation is derived and how NKE-SUSYQM is thereby established. Second, we analyze the fundamental quantum operators and elucidate the complete structure of the supersymmetric algebra within NKE-SUSYQM. Finally, we provide a detailed comparative study that contrasts the positive- and the negative-kinetic-energy SUSYQM, highlighting their key similarities and differences.

Huai‐Yu Wang

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.

Georg Junker

Asim Gangopadhyaya, Jeffry V. Mallow A, Constantin Rasinariu

Luis Grave de Peralta, Arquímedes Ruiz-Columbié

Using the Hamilton-Jacobi and the Lagrange formalisms, a pair of relativistic quantum mechanics equations are obtained by abduction. These equations, in contrast with the Klein-Gordon and other relativistic quantum mechanics equations, have no solutions with both positive and negative kinetic energies. The equation with solutions with only positive kinetic energy values describes a spin-0 particle of mass m, which is moving at relativistic speeds in a scalar potential. The wavefunctions and the energies corresponding to the associated antiparticle can be obtained by solving the other equation, which only has solutions with negative kinetic energy values.