Particle-Field Theory and Its Relativistic Generalization II ( Relativistic Generalization of Micro Harmonic Oscillator and Hydrogen Atom )

TL;DR

This paper extends the particle-field theory to a relativistic framework, solving the relativistic Schrödinger equation for micro-harmonic oscillators and hydrogen atoms, confirming consistency with known relativistic energy corrections.

Contribution

It introduces a relativistic generalization of the particle-field theory and applies it to derive energy spectra of micro-entities like the hydrogen atom.

Findings

Relativistic energy spectrum of micro-harmonic oscillator derived.

Energy spectrum of hydrogen atom obtained and matches first-order relativistic corrections.

The theory maintains Lorentz invariance in the relativistic regime.

Abstract

As a serious attempt for constructing a new foundation for describing micro-entities from a causal standpoint, it was explained before in [1, 2, 3] that by unifying the concepts of information, matter and energy, each micro-entity is assumed to be composed of a probability field joined to a particle called a particle-field or PF system. The relativistic generalization of this theory and its invariance under Lorentz transformation has been proved. In this essay, based on the relativistic generalization of Schrodinger equation derived in [4], we solve the relativistic Schrodinger equation for relativistic micro-harmonic oscillator to find its energy. Also we obtain the energy spectrum of Hydrogen atom that is the main purpose of this paper. We see that the result is completely consistent with the relativistic correction to the Hydrogen's energy in first-order perturbation theory.