Marching toward the eigenvalues: The Canonical Function Method and the Schr\"odinger equation

TL;DR

The paper discusses the Canonical Function Method (CFM), a fast and accurate approach for directly computing eigenvalues of the Schrödinger equation across various quantum problems, including 1D potentials, the hydrogen atom, and Morse potential.

Contribution

It demonstrates the versatility and efficiency of CFM in solving diverse quantum mechanical eigenvalue problems without calculating eigenfunctions.

Findings

CFM provides accurate eigenvalues for 1D potential problems.

CFM effectively solves the 3D hydrogen atom eigenvalues.

CFM efficiently handles Morse potential calculations.

Abstract

The Canonical Function Method (CFM) is a powerful accurate and fast method that solves the Schr\"{o}dinger equation for the eigenvalues directly without having to evaluate the eigenfunctions. Its versatility allows to solve several types of problems and in this work it is applied to the solution of several 1D potential problems, the 3D Hydrogen atom and the Morse potential.