I give new relativistic formulas for kinetic, rest and total energies. The change in kinetic
energy of a particle will be determined as the work done by the spatial part of the Minkowski
four-force. The new relativistic kinetic energy and its relation with the spatial part of the fourmomentum
are given by the expressions similar to its classical equivalents. In particular, I justied
that the rest energy is half of the amount determined by the traditional relation. I present a new
interpretation of the temporal component of the Minkowski four-force.
The nonlinear and novel Bohm-Poisson-Schrödinger equation proposed by us is studied
further. It has solutions leading to repulsive gravitational behavior. An exact analytical expression
for the observed vacuum energy density is obtained. Further results are provided which include
two possible extensions of the Bohm-Poisson equation to the full relativistic regime. Two specific
solutions to the novel Relativistic Bohm-Poisson equation (associated to a real scalar field) are
provided encoding the repulsive nature of dark energy. One solution leads to an exact cancellation
of the cosmological constant, but an expanding decelerating cosmos; while the other solution leads
to an exponential accelerated cosmos consistent with a de Sitter phase, and whose extremely small
cosmological constant is = 3
R2H
, consistent with current observations. We conclude with some
final remarks about Weyl’s geometry.
The main features of the resonance scattering of electrons by molecules are described.
The parameters of the resonances are calculated in the frame of two different approaches: 1) the
theory of collisions in a two-body system (where applicable); 2) the quantum theory of scattering
in a few-body system based on Faddeev-Yakubovsky equations. The results of calculations of the
resonant cross sections of electron and atom collisions with molecules are presented. Obtained results
are compared with the available experimental data and with the results of calculations based on
other approximations. In addition some biological applications (e.g. properties biopolymer molecules)
are presented. Application of the results for determination of biopolymer molecule parameters is
presented.