Asymptotic Iteration Method Solutions to the Relativistic Duffin-Kemmer-Petiau Equation

TL;DR

This paper applies the asymptotic iteration method to find exact and approximate solutions for the relativistic Duffin-Kemmer-Petiau equation, including harmonic, Coulomb, and anharmonic potentials, providing explicit energy eigenvalues and eigenfunctions.

Contribution

It introduces a straightforward analytical approach using the asymptotic iteration method to solve the relativistic Duffin-Kemmer-Petiau equation for various potentials, including perturbative solutions.

Findings

Exact bound state energy eigenvalues for harmonic and Coulomb potentials.

Approximate energy eigenvalues for anharmonic oscillator using perturbation theory.

Explicit eigenfunctions corresponding to the obtained energy levels.

Abstract

A simple exact analytical solution of the relativistic Duffin-Kemmer-Petiau equation within the framework of the asymptotic iteration method is presented. Exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the Coulomb potentials. As a non-trivial example, the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method.