Related papers: Opposite momenta lead to opposite directions
For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite…
We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.
If two point particles collide relativistically in one dimension, and the masses, velocities and gamma factors of the incoming particles are rational numbers, then the velocities and gamma factors of the outgoing particles are rational.…
We analyze the trajectories of a massive particle in one space dimension whose motion is guided by a spin-half wave function that evolves according to the free Dirac equation, with its initial wave function being a Gaussian wave packet with…
An exceptional surface wave can propagate in an isolated direction, when guided by the planar interface of two homogeneous dielectric partnering mediums of which at least one is anisotropic, provided that the constitutive parameters of the…
Feynman contended that the double-slit experiment contained the `only mystery' in quantum mechanics. The mystery was that electrons traverse the interferometer as waves, but are detected as particles. This note was motivated by the question…
Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits…
When propagating through periodically structured media, i. e. photonic crystals, optical waves will be modulated with the periodicity. As a result, the dispersion of waves will no longer behave as in a free space, and so called frequency…
We prove an optimal diffusive decay of the environment viewed by the particle in random walk among random independent conductances, with, as a main assumption, finite second moment of the conductance. Our proof, using the analytic approach…
We address the question of convergence of evolving interacting particle systems as the number of particles tends to infinity. We consider two types of particles, called positive and negative. Same-sign particles repel each other, and…
We show that the collapse of the wave function of an entangled state of two spin 1/2 particles or two photons in the singlet state can be geometrically understood as a change of fibre bundles.
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…
All core collapse supernovae are strongly aspherical. The "Bochum event," with velocity components displaced symmetrically about the principal H$\alpha$ line, strongly suggests that SN 1987A was a bi-polar rather than a uni-polar explosion.…
In general a decay with a missing (not detected) particle can not be fully reconstructed apart from a few exceptions. For example, if the momentum of the decaying particle is known or if the missing energy in an event is measured precisely,…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
It is pointed that we now actually have no enough proofs to prove that time reversal symmetry is universally obeyed in the processes of particle interactions. The analyses show that the time reversal symmetry is obviously violated at least…
The physics involved in the fundamental conservation equations of the spin and orbital angular momenta leads to new laws and phenomena that I disclose. To this end, I analyse the scattering of an electromagnetic wavefield by the canonical…
A light beam changes direction as it enters a liquid at an angle from another medium, such as air. Should the liquid contain molecules that lack mirror symmetry, then it has been predicted by Fresnel that the light beam will not only change…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
The energy spectrum of the extended attractive potential of a crystallographic row for negatively charged particles has quasi-bound states. It follows that a negatively charged particle with small transversal momentum component ($p_{\bot} R…