The factorization method, self-similar potentials and quantum algebras

TL;DR

This paper reviews the Schrödinger factorization method and explores its connections to supersymmetric quantum mechanics, quantum algebras, and various physical models, highlighting recent theoretical developments.

Contribution

It provides a comprehensive overview of the factorization method's applications across multiple areas in quantum physics and mathematical models.

Findings

Connections between factorization and supersymmetric quantum mechanics

Applications to self-similar soliton potentials and quantum algebras

Insights into models like Ising chains and 2D Coulomb gases

Abstract

This is a brief review of the Schrodinger's factorization method and its relations to supersymmetric quantum mechanics and its nonlinear (parastatistical, etc) modifications, self-similar infinite soliton potentials, quantum algebras, coherent states, Ising chains, discretized random matrices and 2D lattice Coulomb gases.