For comparison, Tables 3 and 4 show discrete electronic states for the

Coulomb potential of the charged sphere (1) for Z =1 and Z = 5, respectively.

The Nagaoka potential used to describe the kinetics of particles in the atom is the

Coulomb potential of a geometrical point center of the atom that is given by V(r) = E/r, where r is the distance from the point center and E is a positive charge of the center.

In the scattering matrix theory, the analysis is carried out over the infinite distances from the interaction region both for initial and final states of the system, so that the incoming and outgoing wave functions are plain waves over the whole continuum, and in the derivation of (17), the integral for the Fourier component of the infinite range

Coulomb potential is taken from 0 to [infinity].

During the process of emission and retrapping, the electrons meet a potential energy [phi](x) that is the superposition of the

Coulomb potential of the emitting site and the

Coulomb potential of the retrapping one, and given by

In the first case, substituting the radial part of potential as

Coulomb potential in (13) [26, 27],

As the simplest example, we consider a hydrogen atom in the Earth gravitational field, where we take into account only kinetic and

Coulomb potential energies of an electron in a curved spacetime.

Hassanabadi, "Exact Solutions of Schrodinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and

Coulomb Potential," Communications in Theoretical Physics, vol.

Aldrich, "Variational wave functions for a screened

Coulomb potential," Physical Review A, vol.

For the purpose of finding Gamow function, in area near x=a we can choose linear approximation for

Coulomb potential, such that

We can understand it very well by studying the contributions of the potential parameter b made on the

Coulomb potential. The choice of the negative or positive b determines the attractive

Coulomb potential that is bigger or smaller relatively.

Here the ordinary

Coulomb potential, 1/r, holds and the associated 1/[p.sup.2] decrease of the graph is in accordance with the Rutherford and Mott formulas (see [7], p.

where the first part is the

Coulomb potential with the strength parameter a and the second part is the screening Coulomb and/or Yukawa potential with the strength parameter b.