New Reflections on Electron's Energy and Wavefunction in the Hydrogen Atom

TL;DR

This paper analyzes the zero-energy wavefunction of an electron in the hydrogen atom, revealing it as a quantized classical wavefunction and addressing a previously unexplored aspect of quantum behavior.

Contribution

It provides the first analysis of zero-energy wavefunctions in hydrogen, connecting quantum solutions with classical wavefunctions and uncovering new insights.

Findings

Zero-energy wavefunction is a quantized classical wavefunction

Analysis addresses a gap in literature on zero-energy states

Reveals interesting properties of electron energy in hydrogen

Abstract

Schrodinger's equation predicts something very peculiar about the electron in the Hydrogen atom: its total energy must be equal to zero. Unfortunately, an analysis of a zero-energy wavefunction for the electron in the Hydrogen atom has not been attempted in the published literature. This paper provides such an analysis for the first time and uncovers a few interesting facts, including the fact that a "zero-energy wavefunction" is actually a quantized version of the classical wavefunction that has been known for decades.