Exact Solution of Spherical Harmonic Potential Coupled with E and M fields

TL;DR

This paper applies a tridiagonal representation approach to exactly solve a quantum system with a spherical oscillator potential coupled with electric and magnetic fields, deriving energy spectra and wavefunctions.

Contribution

It extends the tridiagonal representation method to handle perturbed Hamiltonians in quantum systems with electromagnetic coupling.

Findings

Exact energy spectra obtained for the coupled system

Wavefunctions explicitly derived for the perturbed system

Method demonstrates potential for solving similar quantum problems

Abstract

Using the technique of tridiagonal representation approach; for the first time, we extend this method to study quantum systems with literally perturbed Hamiltonians. Specifically, we consider a quantum system in a 3D spherical oscillator symmetric potential function coupled with an electric and a magnetic field. We obtain the energy spectrum and wavefunction in the two cases.