Related papers: Quantum and classical solutions for free particle …
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
We consider a scalar particle in a background formed by two counter-propagating plane waves. Two cases are studied: i) dynamics at a magnetic node and ii) zero initial transverse canonical momentum. The Lorentz and Klein-Gordon equations…
Recently the spectacular result was derived quantum mechanically that the total angular momentum of photons in light beams with finite lateral extensions can have half-integer quantum numbers. In a circularly polarized Gauss light beam it…
A rigorous application of the correspondence rules shows that the operator of the angular momentum of a quantum particle---corresponding to the classical magnitude $\mathbf{l}= m \mathbf{r} \wedge \mathbf{v}$---is given by…
We propose classical equations of motion for a charged particle with magnetic moment, taking radiation reaction into account. This generalizes the Landau-Lifshitz equations for the spinless case. In the special case of spin-polarized motion…
In an earlier letter [Ducharme \textit{et al.} Phys. Rev. Lett. \textbf{126}, 134803 (2021)], a solution to the Dirac equation for a relativistic Gaussian electron beam showed that for a diverging beam the spin of each electron is the sum…
Building upon our recently established correspondence between quantum cosmology and the hydrogen atom [1], we investigate the specific sector of a negative cosmological constant ($\Lambda < 0$) in a flat FLRW universe with dust. While the…
The question how to quantize a classical system where an angle phi is one of the basic canonical variables has been controversial since the early days of quantum mechanics. The problem is that the angle is a multivalued or discontinuous…
In two recent papers exact Hermite-Gaussian solutions to relativistic wave equations have been obtained for both electromagnetic and particle beams that include Gouy phase. The solutions for particle beams correspond to those of the…
We investigate the problem of classical big bang singularity in a plane-symmetric Bianchi type-I universe within the Wheeler-DeWitt (WDW) framework of quantum gravity. To address the problem of time, we employ the Page-Wootters formalism,…
We extend the canonical formalism for the motion of $N$-particles in lineal gravity to include charges. Under suitable coordinate conditions and boundary conditions the determining equation of the Hamiltonian (a kind of transcendental…
Lie-Poisson electrodynamics describes the semi-classical limit of non-commutative $U(1)$ gauge theory, characterized by Lie-algebra-type non-commutativity. We focus on the mechanics of a charged point-like particle moving in a given gauge…
This paper is concerned with the study of one-body dissipation effects in idealized models resembling a nucleus. In particular, we study the quantum mechanics of a free particle that collides elastically with the slowly moving walls of a…
Inspired by the electromagnetic duality, we propose an approach to realize the fractional angular momentum by using a cold atom which possesses a permanent magnetic dipole momentum. This atom interacts with two electric fields and is…
Recently, Wilson loops with the shape of a double helix have played an important role in studying large spin operators in gauge theories. They correspond to a quark and an anti-quark moving in circles on an S3 (and therefore each of them…
The geometry of a billiard boundary fundamentally governs its dynamics, ranging from integrable to mixed and fully chaotic regimes. Bean- and peanut-shaped billiards have varying curvature with both focusing and defocusing walls without a…
A new Bateman-Hillion solution to the Dirac equation for a relativistic Gaussian electron beam taking explicit account of the $4$-position of the beam waist is presented. This solution has a pure Gaussian form in the paraxial limit but…
Intimate though the connection is between orbital angular momentum and intrinsic spin, there are differences between them the two quantities. One of them is the fact that while orbital angular momentum has a wave-mechanics description by…
We study the motion of classical particles confined in a two-dimensional "nuclear" billiard whose walls undergo periodic shape oscillations according to a fixed multipolarity. The presence of a coupling term in the single particle…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…