Solution of the relativistic Dirac-Morse problem

Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version of the S-wave Morse potential. This is accomplished by adding a simple exponential potential term to the Dirac operator, which in the nonrelativistic limit reproduces the usual Morse potential. The relativistic bound states spectrum and spinor wavefunctions are obtained.Comment: Erratum: The last statement above Eq. (1) is now corrected and replaced by two new statement

Magnetic field-induced electric quadrupole moment in the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength $B$ of the perturbing field, the only electric multipole moment induced by the field in the ground state of the atom is the quadrupole one. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825; erratum 30 (1997) 2747], we derive a closed-form expression for the induced electric quadrupole moment. The result contains the generalized hypergeometric function $_{3}F_{2}$ of the unit argument. Earlier calculations by other authors, based on the non-relativistic model of the atom, predicted in the low-field region the quadratic dependence of the induced electric quadrupole moment on $B$.Comment: LaTeX2e, 9 page

Integral equation formulation of the spinless Salpeter equation

The spinless Salpeter equation presents a rather particular differential operator. In this paper we rewrite this equation into integral and integro-differential equations. This kind of equations are well known and can be more easily handled. We also present some analytical results concerning the spinless Salpeter equation and the action of the square-root operator.Comment: 13 pages, no figure. ReVTeX file. To appear in J. MATH. PHY