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Generalization of Klein Gordon Equation in a Curved Space and Harmonic Oscillator's Solution
Ist Teil von
NeuroQuantology, 2023-01, Vol.21 (6), p.1795
Ort / Verlag
Bornova Izmir: NeuroQuantology
Erscheinungsjahr
2023
Link zum Volltext
Quelle
EZB Free E-Journals
Beschreibungen/Notizen
In this work the equation of motion of a particle in a curved space time which proved that all fields deform the space time as derived by many researchers was used to derive Klein Gordon equation in a curved space time. This expression indicates that the rest mass is potential dependent. This confirms the recent observations of the dependence of the rest mass of elementary particles by the potential. It also confirms the effective mass relationships in material science, which was proposed to explain the observed change of the electron mass by the crystal and bulk matter internal potential. This expression confirms the calculations of the loops contributions to the mass term, which also include the effect of the potential on the rest mass. The time dependent rest mass was incorporated into the Klein Gordon equation. The results obtained for harmonic oscillator solution gives frequency and rest mass dependent terms. The appearance of the additional rest mass term beside the frequency term confirms the particle wave duality of the atomic entities. Where the rest mass term exhibits the particle nature while the frequency dependent term manifests the wave nature. The association of the curved space with the potential which is responsible for the appearance of the frequency term indicates that the space curvature represents a new ether that can generate gravitational waves produced by oscillating masses