Energy eigenvalues of spherical symmetric potentials with relativistic corrections: analytic results

Abstract

Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including the relativistic corrections. The energy eigenvalues of spherical symmetric potentials for two-particle bound state systems with relativistic corrections are analytically derived. The energy spectra of linear and funnel potentials with orbital and radial excitations are determined. The energy spectrum of a superposition of Coulomb and Yukawa potentials is also determined. Our result shows that the energy spectrum with the relativistic corrections for the linear, harmonic oscillator and funnel potentials is smaller than the upper boundaries for the energy spectrum established in the framework of the spinless Salpeter equation for the orbital and radial excited states. The relativistic corrections to the energy spectrum of a superposition of the attractive Coulomb potential and the Yukawa (exponentially screened Coulomb) potentials are very small.

Determination of the energy spectrum of a three-body Coulomb system with relativistic corrections

“…In the framework of our approach, we have considered the two-body Coulomb systems [6,7] and determined the energy spectrum and WF by taking into account relativistic corrections. We now define the ground-state energy of the three-body Coulomb system with charges Z 1 e, Z 2 e, and −Z 3 e in the framework of our approach.…”

“…In our approach [6][7][8], the mass of the bound state is determined by the asymptotic behavior of the correlation function of the corresponding currents with the necessary quantum numbers. The correlation function, which is expressed in terms of the Green's function is represented as a functional integral, which allows one to allocate the necessary asymptotic behavior, and the averaging over the external gauge field can be performed accurately.…”