Calculation of quantum eigens with geometrical algebra rotors

TL;DR

This paper introduces a geometric algebra rotor-based method for calculating quantum eigenvalues and eigenspinors, simplifying the process by replacing traditional quantization conditions with vector norm preservation, demonstrated through various examples.

Contribution

It presents a novel computational approach using geometric algebra rotors to find quantum eigenvalues and eigenspinors more simply than traditional methods.

Findings

Successfully applied to monolayer graphene and quantum well spin systems

Extended to coupled two-level atoms and bilayer graphene

Simplifies eigenvalue computation in quantum mechanics

Abstract

A practical computation method to find the eigenvalues and eigenspinors of quantum mechanical Hamiltonian is presented. The method is based on reduction of the eigenvalue equation to well known geometric algebra rotor equation and, therefore, allows to replace the usual det(H-E)=0 quantization condition by much simple vector norm preserving requirement. In order to show how it works in practice a number of examples are worked out in Cl_{3,0} (monolayer graphene and spin in the quantum well) and in Cl_{3,1} (two coupled two-level atoms and bilayer graphene) algebras.