Related papers: On the Ehrenfest theorem and centroids of relativi…
Ehrenfest theorem is proven in relativistic quantum theory of charged particles, moving under the influence of an external electromagnetic field. In order to extend the classic Ehrenfest result to the relativistic domain we bypassed the…
We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…
The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. However, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct.…
We demonstrate that the Einstein relation for the diffusion of a particle in the random energy landscape with the Gaussian density of states is an exclusive 1D property and does not hold in higher dimensions. We also consider the analytical…
This paper develops a general method to construct Ehrenfest-like relations for Lagrangian field theories when an external, coordinate-dependent scalar potential is applied. To do so, we derive continuity equations in which the spatial and…
Based on the assumption that the probability density of finding a free particle is independent of position, we infer the form of the eigenfunction for the free particle, $\bra{x} p > = \exp(ipx/\hbar)/\sqrt{2\pi\hbar}$. The canonical…
We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This…
The Ehrenfest time scale in quantum transport separates essentially classical propagation from wave interference and here we consider its effect on the transmission and reflection through quantum dots. In particular we calculate the…
The relations among the components of the exit momenta of ultrarelativistic electrons scattered on a strong electromagnetic wave of a low (optical) frequency and linear polarization are established using the exact solutions to the equations…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
We give the free energy of equilibrium relativistic matter subject to external gravitational and electromagnetic fields, to one-derivative order in the gradients of the external fields. The free energy allows for a straightforward…
For a particle in a box, the operator $-i\partial_x$ is not self-adjoint and thus does not qualify as the physical momentum. As a result, in general the Ehrenfest theorem is violated. Based upon a recently developed new concept for a…
The notion of Einstein causality, i.e. the limiting role of the velocity of light in the transmission of signals, is discussed. It is pointed out that Nimtz and coworkers use the notion of signal velocity in a different sense from Einstein…
Coincidence scattering of polarized electrons from nuclei with polarization transfer to outgoing nucleons is studied within the context of relativistic mean field theory. Effects introduced by the dynamical enhancement of the lower…
Attempts to explain the refraction of light in dispersive media in terms of a photon or "corpuscular" model have heretofore been unable to account for the observed decrease in the speed of light as it passes from air into a region of higher…
It is shown that for a specific choice of a particular solution of the relativistic wave equation, it falls into the Helmholtz equation and the Klein -Gordon equation. In this case, the squares of the rest masses of the particle with the…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
In this work a new mechanics will be studied which is based on the hypothesis that the change of linear momentum of a particle happens as a discrete pulses. By using this hypothesis and by considering Newton's relation between energy and…
A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle…