The two-dimensional (2D) relativistic bound states of a spinless particle placed in scalar
Relativistic wave equations such as Dirac and Klein-Gordon equations have been of much concern for theoretical physicists [
Over the past few years, there has been an increasing interest in obtaining the exact solutions to the spinless KG particles exposed to different potential models [
One of the potentials that has received much attention in particle physics was the Cornell (Coulomb plus linear) potential. It has been used successfully in models describing binding states of heavy quarks [
The ground state energy (
Very recently, we have studied the scalar charged particle in scalar-vector (harmonic oscillator plus Cornell) potentials with and without external magnetic and Aharonov-Bohm flux fields [
The aim of this work is to extend [
The structure of this paper is as follows. In Section
The Klein-Gordon atom for the spinless particle with mass
The energy states require that
Hence, the Schrödinger-type equation with unequal scalar-vector Cornell potential can be written as
To obtain the recurrence relation which can connect various expansion coefficients
We can find the wave function in (
Notice that the present model has been solved in 2D space with an external uniform magnetic field since it is perpendicular to the plane where the vector and scalar Cornell potentials have the dimensions of
In this section, we will obtain the energy levels with and without external magnetic field and AB flux field and the energy levels in three dimensional (3D) space. Two special cases of much interest are considered, namely, the Coulomb and harmonic oscillator.
Firstly, let us consider the present system without external fields; that is,
If the vector potential is taken zero, that is,
Fourthly, if the potential parameter
Fifthly, if potential parameter
To sum up, in this paper, we used the wave function ansatz method to study the bound state solutions of the KG equation in 2D space for unequal mixture of the Cornell potential with and without external magnetic and AB flux fields of arbitrary Larmor frequency
It is noticed that the solution of KG with pure scalar Cornell potential provides the general bound state solution for the well-known Cornell plus harmonic oscillator solution for a spinless particle. The bound state solution exists for the relativistic spin-
The method is effective in solving the singular Cornell potential and produces the desired results. To test the accuracy of our results, specific choices of the potential parameters recover the results of the exactly solvable Coulomb, harmonic oscillator, and Kratzer potentials.
The author thanks the kind referees for their suggestions and comments which have greatly improved the paper. This work is partially supported by the Scientific and Technological Research Council of Turkey.