A calculation with a bi-orthogonal wavelet transformation

TL;DR

This paper introduces a bi-orthogonal wavelet transformation that relaxes traditional constraints and applies it to quantum physics, specifically calculating eigenvalues and eigenfunctions of relativistic Hydrogen-like atoms.

Contribution

It presents a novel use of bi-orthogonal basis in continuous wavelet transforms, expanding their applicability to quantum mechanical problems.

Findings

Successfully determined eigenvalues of the relativistic Hydrogen-like atom Hamiltonian.

Derived radial eigenfunctions using the bi-orthogonal wavelet approach.

Demonstrated the method's potential for quantum physics applications.

Abstract

We explore the use of bi-orthogonal basis for continuous wavelet transformations, thus relaxing the so-called admissibility condition on the analyzing wavelet. As an application, we determine the eigenvalues and corresponding radial eigenfunctions of the Hamiltonian of relativistic Hydrogen-like atoms.