Coulomb Potential

Stephen P. Martin

V. V. Dodonov, Vladimir I. Man’ko, D. L. Osipov

Ch. Grosche

The path integral for the potential is evaluated in three different coordinate systems, i. e. in cartesian coordinates, in polar coordinates and in parabolic coordinates. The equivalence between the different approaches is shown and in each case the energyspectrum and the wave functions are explicitly calculated. Furthermore we discuss special cases, including the ring-potential, the Coulomb potential with an Aharonov-Bohm solenoid, and the genuine Coulomb problem. We also point out the separability of the path integral formulation of the ring-potential in spheroidal coordinates, and of the Coulomb potential in spheroidal and spheroconical coordinates, respectively.

Eric Hand

John D. Dollard

It is shown that the operator U(±)c(t) defined by Muhlerin and Zinnes [J. Math.Phys.11,1402 (1970)] in their account of Coulomb potential scattering theory is not an isometry when the Coulomb potential is weak enough. It is opined that for this reason their account of Coulomb potential scattering theory does not have a straightforward physical interpretation.