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 , 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.