Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Modified Fundamental Equations of Quantum Mechanics in Symmetric Forms

Version 1 : Received: 24 August 2021 / Approved: 25 August 2021 / Online: 25 August 2021 (10:50:21 CEST)

How to cite: Wang, H. The Modified Fundamental Equations of Quantum Mechanics in Symmetric Forms. Preprints 2021, 2021080486 (doi: 10.20944/preprints202108.0486.v1). Wang, H. The Modified Fundamental Equations of Quantum Mechanics in Symmetric Forms. Preprints 2021, 2021080486 (doi: 10.20944/preprints202108.0486.v1).

Abstract

Up to now, Schrödinger equation, Klein-Gordon equation (KGE) and Dirac equation are believed the fundamental equations of quantum mechanics. Schrödinger equation has a defect that there is no NKE solutions. Dirac equation has positive kinetic energy (PKE) and negative kinetic energy (NKE) branches. Both branches should have low momentum, or nonrelativistic, approximations: one is Schrödinger equation and the other is NKE Schrödinger equation. KGE has two problems: it is an equation of second time derivative, and calculated density is not definitely positive. To overcome the problems, it should be revised as PKE and NKE decoupled KGEs. The fundamental equations of quantum mechanics after the modification have at least two merits. They are of unitary in that everyone contains the first time derivative and are symmetric with respect to PKE and NKE. This reflects the symmetry of the PKE and NKE matters, as well as matter and dark matter, of our universe. The problems of one-dimensional step potentials are resolved by means of the modified fundamental equations for a nonrelativistic particle.

Keywords

Dirac equation; Klein-Gordon equation; Schrödinger equation; negative kinetic energy; Decoupled Klein-Gordon equation; negative kinetic energy Schrödinger equation

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