Related papers: Classical position probability densities for spher…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
A simple analytical expression, which closely approximates the Coulomb potential between two uniformly charged spheres, is presented. This expression can be used in the optical potential semiclassical analyses which require that the…
Severe methodological and numerical problems of the traditional quantum mechanical approach to the description of molecular systems are outlined. To overcome these, a simple alternative to the Born-Oppenheimer approximation is presented on…
An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…
The classical dynamics of particles with (non-)abelian charges and spin moving on curved manifolds is established in the Poisson-Hamilton framework. Equations of motion are derived for the minimal quadratic Hamiltonian and some extensions…
A quasi classical approximation to quantum mechanical scattering in the Moeller formalism is developed. While keeping the numerical advantage of a standard Classical--Trajectory--Monte--Carlo calculation, our approach is no longer…
Classical radiation equilibrium (the blackbody problem) is investigated by the use of an analogy. Scaling symmetries are noted for systems of classical charged particles moving in circular orbits in central potentials V(r)=-k/r^n when the…
We study, in the semi-classical approximation, the convergence of the quantum density and the quantum action, solutions to the Madelung equations, when the Planck constant h tends to 0. We find two different solutions which depend to the…
Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…
A perturbation method to analytically describe the dynamics of a classical spinning particle, based on the Mathisson-Papapetrou-Dixon (MPD) equations of motion, is presented. By a power series expansion with respect to the particle's spin…
The in-in effective action formalism is used to derive the semiclassical correction to Einstein's equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
In the framework of Nelson stochastic quantization we derive exact non-stationary states for a class of time-dependent potentials. The wave-packets follow a classical motion with constant dispersion. The new states thus define a possible…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a…
A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action. This formulation is extended to the quantum…
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
A phenomenological model of the time evolution of a particle wavepacket is presented that is subject to scattering event with small momentum transfer. It is suited for three dimensions and allows for an additional potential. For a random…