Schrodinger's Field Equation

TL;DR

This paper investigates the energies and angular momentum of electron states in the hydrogen atom using operator formalism, revealing insights into electron field representation and spinning dynamics.

Contribution

It introduces a field-based interpretation of electron energies and spins, analyzing multiple states with operator methods and confirming energy rules.

Findings

Total energies follow the 1/n^2 rule.

Angular momentum analysis yields a field spinning rate.

Dynamic kinetic energy matches calculations based on spinning rate.

Abstract

The intrinsic and dynamic kinetic energies, and the potential energies of electron states in the hydrogen atom, were determined using the operator formalism in the Schrodinger nonrelativistic equation. Intrinsic energies were determined using the momentum operator, while the additional dynamic energies of the spinning fields were determined using the angular momentum operator. All 10 states up to the principal quantum number n = 3 and all m states of n = 7, l = 3 were analyzed. The two forms of kinetic energy can only be explained with an electron field representation. All total kinetic and potential energies conformed with the well known 1/n^2 rule. Angular momentum analysis of the 2P1/2 states provided a field spinning rate; in addition, the dynamic kinetic energy of the spinning field determined by both operator analysis and explicit calculation based on the spinning rate gave the same energy results.