# Analytical solution of two-body spinless Salpeter equation for Hellmann potential

@article{Arda2017AnalyticalSO, title={Analytical solution of two-body spinless Salpeter equation for Hellmann potential}, author={Altuğ Arda}, journal={Indian Journal of Physics}, year={2017}, volume={91}, pages={903-907} }

Approximate bound state solutions of the spinless Salpeter equation for the Hellmann potential are studied for heavy particles. By using functional analysis method, an analytical expression for the energy levels, and the corresponding eigenfunctions of the system are obtained in terms of the hypergeometric functions. The analytical results for the Yukawa and Coulomb potentials are also studied as special cases.

## 4 Citations

### The spinless relativistic Hellmann problem

- PhysicsInternational Journal of Modern Physics A
- 2019

We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as…

### On an approximation of the two-body spinless Salpeter equation

- MathematicsThe European Physical Journal Plus
- 2018

Abstract.In recent years several published works have aimed at finding approximate analytical solutions of the two-body spinless Salpeter equation, starting from the approximation $\sqrt{p^{2}+m^{2}}…

### Investigating Some Diatomic Molecules Bounded by the Two-Dimensional Isotropic Oscillator plus Inverse Quadratic Potential in an External Magnetic Field

- PhysicsAdvances in High Energy Physics
- 2022

We investigate the nonrelativistic magnetic effect on the energy spectra, expectation values of some quantum mechanical observables, and diamagnetic susceptibility for some diatomic molecules bounded…

### Approximate Scattering State Solutions of DKPE and SSE with Hellmann Potential

- PhysicsAdvances in High Energy Physics
- 2018

We study the approximate scattering state solutions of the Duffin-Kemmer-Petiau equation (DKPE) and the spinless Salpeter equation (SSE) with the Hellmann potential. The eigensolutions, scattering…

## References

SHOWING 1-10 OF 39 REFERENCES

### Exact solutions of the Spinless-Salpeter equation under Kink-Like potential

- Physics
- 2013

The exact solution of Spinless-Salpeter equation (SSE) in the presence of Kink-Like potential is investigated. By using the basic concepts of the supersymmetric quantum mechanics (SUSYQM) formalism…

### Solutions of the Two-Body Salpeter Equation Under an Exponential Potential for Any l State

- Physics
- 2012

The two-body Salpeter equation is analytically solved for an interaction of exponential form. We see that after using appropriate approximations, the problem appears as the well-known Morse potential…

### Exact analytical treatment of the asymmetrical spinless Salpeter equation with a Coulomb-type potential

- Physics
- 2014

An exact analytical treatment is presented, in the momentum space, for the one-dimensional spinless Salpeter equation describing two particles with unequal masses interacting via a Coulomb-type…

### Bound-States of the Spinless Salpeter Equation for the PT-Symmetric Generalized Hulthén Potential by the Nikiforov-Uvarov Method

- Mathematics
- 2018

The one-dimensional spinless Salpeter equation has been solved for the PT -symmetric generalized Hulthén potential. The Nikiforov-Uvarov (NU) method which is based on solving the second-order linear…

### Analytical treatment of the one-dimensional Coulomb problem for the spinless Salpeter equation

- Physics
- 2009

Using the momentum space representation, we present an analytical treatment of the one-dimensional spinless Salpeter equation with a Coulomb interaction. The exact bound-state energy equation is…

### Energy bounds for the spinless Salpeter equation: harmonic oscillator

- Mathematics
- 2000

We study the eigenvalues nl of the Salpeter Hamiltonian H = β(m2 + p2)1/2 + vr2, v>0, β>0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided,…

### A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential

- Physics
- 2013

By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter (SS) equation with the Woods-Saxon…

### Bethe-Salpeter equation for non-self conjugate mesons in a power-law potential

- Physics
- 1993

We develop an approach to the solution of the spinless Bethe-Salpeter equation for the different-mass case. Although the calculations are developed for spinzero particles in any arbitratry…

### SEMIRELATIVISTIC TREATMENT OF BOUND STATES

- Physics
- 1998

This review discusses several aspects of the semirelativistic description of bound states by the spinless Salpeter equation (which represents the simplest equation of motion incorporating…