Quantum Mechanics without Complex Numbers: A Simple Model for the Electron Wavefunction Including Spin

TL;DR

This paper proposes a real-space, spin-inclusive model of the electron wavefunction that avoids complex numbers, providing an intuitive physical picture while satisfying the Schrödinger equation.

Contribution

It introduces a simple real-space model for the electron wavefunction with spin, replacing complex numbers with a transverse wave with helicity rotating at mc^2/h.

Findings

Model satisfies the Schrödinger equation

Provides an intuitive physical picture of electron spin

Extends to include spin in a real-space framework

Abstract

A simple real-space model for the electron wavefunction is suggested, based on a transverse wave with helicity, rotating at mc^2/h. The mapping of the real two-dimensional vector phasor to the complex plane permits this to satisfy the standard time-dependent Schroedinger equation. This model is extended to provide an intuitive physical picture of electron spin. Implications of this model are discussed.