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Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, this leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical…
A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical…
We investigate the spin dynamics of a dipole-coupled system by comparing a direct solution of the Schrodinger equation for quantum spins with simulations of classical spins. Although classical spins have long been used in microscopic spin…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
We analyze how non-relativistic effective models for the magnetic coupling of a spin to the electromagnetic field (proportional to $\hat{\boldsymbol{\sigma}}\cdot \boldsymbol{B}$) emerge from a full quantum field theoretical description of…
In evaluating differential cross section of elastic scattering, different theories were applied to low-momentum and relativistic particles. For low-momentum motion, Lippmann-Schwinger scattering equation was applied, called fundamental…
Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and…
We propose a general derivation of differential cross section in quark-quark scatterings at fixed impact parameters. The derivation is well defined and free of ambiguity in the conventional one. The approach can be applied to a variety of…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
The classical rotation is not self-consistent in the framework of the special theory of relativity. the Relativistic rotation is obtained, which takes the relativistic effect into account. It is demonstrated that the angular frequency of…
Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
The definition of weak equivalence principle of quantum matter is an open problem at present. In order to reflect the probability of quantum system in the quantum version of weak equivalence principle, we proposed a quantum weak equivalence…
By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained.…
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…
A first-principles theory of resonant magnetic scattering of x rays is presented. The scattering amplitudes are calculated using a standard time-dependent perturbation theory to second order in the electron-photon interaction vertex. In…
This thesis reports on work undertaken in comparing the effects of the phenomenon of radiation reaction in classical and quantum theories of electrodynamics. Specifically, it is concerned with the prediction of the change in position of a…
Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor…
In this paper the problem of noncommutative elastic scattering in a central field is considered. General formulas for the differential cross-section for two cases are obtained. For the case of high energy of an incident wave it is shown…
Problems of interacting quantum magnetic moments become exponentially complex with increasing number of particles. As a result, classical equations are often used but the validity of reduction of a quantum problem to a classical problem…