‎In this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular Sturm-Liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎Also Weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

To search the infrared behaviour of the propagator in three dimensional QED ordinary perturbative method is not appropreate because of its bad infrared divergences[4].Assuming spectral representation and LSZ reduction formula,we evaluate the infrared behaviour or the mass singularity of the fermion propagator in three dimensional QED as in four dimension.In quenched case with bare photon mass w...

To search the infrared behaviour of the propagator in three dimensional QED ordinary perturbative method is not appropreate because of its bad infrared divergences[4].Assuming spectral representation and LSZ reduction formula,we evaluate the infrared behaviour or the mass singularity of the fermion propagator in three dimensional QED as in four dimension.In quenched case with bare photon mass w...

To search the infrared behaviour of the propagator in three dimensional QED ordinary perturbative method is not appropreate because of its bad infrared divergences[4].Assuming spectral representation and LSZ reduction formula,we evaluate the infrared behaviour or the mass singularity of the fermion propagator in three dimensional QED as in four dimension.In quenched case with bare photon mass w...

For n ∈ {2, 3} we prove minimax characterisations of eigenvalues in the gap of the n dimensional Dirac operator with an potential, which may have a Coulomb singularity with a coupling constant up to the critical value 1/(4 − n). This result implies a socalled Hardy-Dirac inequality, which can be used to define a distinguished self-adjoint extension of the Coulomb-Dirac operator defined on C0 (R...

The method of Gaussian wave packet (GWP) propagation introduced by Heller is a popular tool for doing time dependent quantum mechanical calculations in particular in molecular and in nuclear physics. We show that this method is also applicable to atomic systems. We concentrate on the H-atom in a strong magnetic field, where a well-known regularization is used to remove the singularity. The Coul...

The starting point is the problem of finding the interaction energy of two coinciding homogeneous cubic charge distributions. The brute force method of subdividing the cube into N sub-cubes and doing the sums results in slow convergence because of the Coulomb singularity. Using symmetry and algebra the Coulomb singularities can be eliminated. This leads to an accurate numerical algorithm as wel...