a saddle point variational (spv ) method was applied to the dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. the effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. the cornell pot...

The equation of motion for the first-order density matrix ~1DM! is constructed for interacting electrons moving under the influence of given external scalar and vector potentials. The 1DM is coupled there to the 2DM by means of the electron-electron interaction. This equation is then employed to obtain the differential virial equation for interacting electrons moving in a magnetic field of arbi...

Lorentz transmission electron microscopy (TEM) observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials. Vector field electron tomography (VFET) can be used to reconstruct electromagnetic potentials of the nanoparticles from their corresponding LTEM images. The VFET approach is based on the conventional filtered back projection approach to tomograp...

We introduce a translational and rotational invariant local representation for vector fields, which can be employed in the construction of machine learning energy models solids molecules. This allows us to describe, on same footing, fluctuations due atomic motion, longitudinal transverse excitations field, their mutual interplay. The formalism then applied physical systems where total is determ...