Related papers: Constructing Wavefunctions for One-Body and Two-Bo…
We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…
This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic…
We present a new methodology to analyze complicated multi-physics simulations by introducing a fictitious parameter. Using the method, we study quantum mechanical aspects of an organic molecule in water. The simulation is variationally…
Almost a century after the development of quantum mechanics, we still do not have a consensus on the process of collapse of wavefunctions. Some theories require the intervention of a conscious observer while some see it as a stochastic…
The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been…
The rotation of the bodies and the eccentricity of the orbit have significant effects on the emitted gravitational radiation of binary systems. This work focuses on the evaluation of the gravitational wave polarization states for spinning…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
Using the mathematical theory of shape calculus as tool, we perform a rigorous investigation of the virtual work principle for the computation of electromagnetic forces in static settings. The main goal is to shed light on the widely held…
The problem of a single electron in a magnetic field is revisited from first principles. It is shown that the standard quantization, used by Landau, is inconsistent for this problem, whence Landau's wave functions spontaneously break the…
In this paper we propose an approach to the problem of two body motion in classical electrodynamics that takes into account the electromagnetic radiation and the radiation reaction forces. The resulting differential equations are solved…
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case,…
A method is presented which allows the exact construction of conserved (i.e. divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric…
In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…
In this work, which is based on an essential linear analysis carried out by Christodoulou, we study the evolution of tidal energy for the motion of two gravitating incompressible fluid balls with free boundaries obeying the Euler-Poisson…
Different numbers of self-gravitating particles (in different types of periodic motion) are most likely to generate very different shapes of gravitational waves, some of which, however, can be accidentally almost the same. One such example…
In the expansive nondecelerative universe model, creation of matter occurs due to which the Vaidya metrics is applied. This fact allows for localizing gravitational energy and calculating the energy of gravitational waves using an approach…
We experimentally obtained a direct image of the nuclear wave functions of {H_2}^+ by dissociating the molecule via electron attachment and determining the vibrational state using the COLTRIMS technique. Our experiment visualizes the nodal…
In this paper we continue the study, started in [1], of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the Thirties. In particular we show that the introduction of the KvN Hilbert space of…
Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…