Related papers: Superluminal matter waves
The Dirac oscillator is an exactly soluble model recently introduced in the context of many particle models in relativistic quantum mechanics. The model has been also considered as an interaction term for modelling quark confinement in…
The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…
Einstein's theory of special relativity(SR) and the principle of causality imply that the speed of any moving object can not exceed that of light in a vacuum($c$).However,there were many attempts in literature discussing the particle moving…
In this article, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles, by a careful treatment of temporal observables in quantum theory and through a precise application of the duality between…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from…
We consider the model of Dirac fermions coupled to gravity as proposed in \cite{VolovikBH}, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates…
Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave packet formalism. We demonstrate that whereas the Dirac system is causal, the…
The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular…
Some recent experiments, performed at Berkeley, Cologne, Florence and Vienna led to the claim that something seems to travel with a speed larger than the speed c of light in vacuum. Various other experimental results seem to point in the…
Searching for new states of matter and unusual quasiparticles in emerging materials and especially low-dimensional systems is one of the major trends in contemporary condensed matter physics. Dirac materials, which host quasiparticles which…
Classical mechanical treatment of charged particle beam optics is so far very satisfactory from a practical point of view in applications ranging from electron microscopy to accelerator technology. However, it is desirable to understand the…
In this paper we present a pedestrian review of the theoretical fact that all relativistic wave equations possess solutions of arbitrary velocities $0 \leq v < \infty$. We discuss some experimental evidences of $v \geq c$ transmission of…
The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total…
In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle…
Almost 60 years ago Dicke introduced the term superradiance to describe a signature quantum effect: N atoms can collectively emit light at a rate proportional to N^2. Even for moderate N this represents a significant increase over the…
The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…
We consider a single particle which is bound by a central potential and obeys the Dirac equation. We compare two cases in which the masses are the same but Va < Vb, where V is the time-component of a vector potential. We prove generally…
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable…
In this note we present an example from undergraduate quantum mechanics designed to highlight the versatility of the Dirac $\delta$-function. Namely, we compute the expectation value of the Hamiltonian of a free-particle in a state…