Normalized eigenfunctions of parametrically factored Schroedinger equations

TL;DR

This paper reviews the use of Riccati-based factorizations for Schrödinger equations, focusing on eigenfunction normalization in Darboux-deformed Hamiltonians, extending prior methods to new quantum systems.

Contribution

It introduces a method for normalizing eigenfunctions of parametrically factored Schrödinger equations using Riccati solutions, building on earlier factorization techniques.

Findings

Eigenfunction normalization is achievable for Darboux-deformed Hamiltonians.

The Riccati-based factorization approach extends to various quantum systems.

The method improves the understanding of eigenfunction properties in deformed potentials.

Abstract

The factorizations using the general Riccati solution constructed from a given particular solution by means of the Bernoulli ansatz initiated in 1984 by Mielnik and Fernandez C. for the cases of the quantum harmonic oscillator and the radial Hydrogen equation, respectively, are briefy reviewed. The issue of the eigenfunction normalization of the obtained one-parameter Darboux-deformed Hamiltonians is addressed here.