The Schrodinger equation and negative energies

TL;DR

This paper introduces a nonrelativistic wave equation for electrons that incorporates negative-energy states, extending traditional quantum mechanics and solving it for classic cases to include these states.

Contribution

It presents a novel nonrelativistic wave equation that accounts for negative-energy eigenstates, expanding the scope of quantum electron models.

Findings

Reproduces the Pauli equation with negative-energy states

Provides solutions for three classical quantum systems

Extends quantum theory to include negative energies

Abstract

We present a nonrelativistic wave equation for the electron in (3+1)-dimensions which includes negative-energy eigenstates. We solve this equation for three well-known instances, reobtaining the corresponding Pauli equation (but including negative-energy eigenstates) in each case.