Asymptotic iteration method solutions to the relativistic Duffin-Kemmer-Petiau equation

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.

Quantum dynamics of scalar bosons in a cosmic string background

“…Although the formalisms are equivalent in the case of minimally coupled vector interactions [5][6][7], the DKP formalism enjoys a richness of couplings not capable of being expressed in the KG and Proca theories [8,9]. Recently, there has been increasing interest in the so-called DKP oscillator [10][11][12][13][14][15][16][17][18][19]. The DKP oscillator considering minimal length [20,21] and noncommutative phase space [22][23][24][25] have also appeared in the literature.…”

“…The name distinguishes it from the system called a DKP oscillator with Lorentz tensor couplings of Ref. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

An alternative solution of diatomic molecules

“…Among these methods, AIM, which was developed by H. Ciftci in 2003 to solve the Schrödinger like second order differential equation, has been used in many field of physics due to the simplicity in obtaining the energy eigenvalues and corresponding eigenfunctions [35][36][37][38][39][40]. To apply the method, the asymptotic wavefunction form should be proposed after substituting the potential in Schrödinger equations with the AIM then applied to calculate the spectrum of potentials.…”

Approximate Complete Solutions of DKP Equation under a Vector Exponential Interaction via a Pekeris-Type Approximation

“…In addition, the DKP equation is richer in the investigation of interactions and is even closer to some experimental data in comparison with KG or Proca equations 15-20 . Moreover, besides cosmology and gravity, this equation has been tested in many branches of physics including particle and nuclear physics 21-25 . As usual, the most appealing case studies are Coulomb and quadratic terms 26-28 , and other ones including the woods-Saxon and Hulthen are investigated by different 2 ISRN High Energy Physics approaches as well [29][30][31][32] . Within the present work, we first review the DKP equation.…”