Related papers: Spin-orbit coupling and the conservation of angula…
The Bertrand theorem concluded that; the Kepler potential, and the isotropic harmonic oscillator potential are the only systems under which all the orbits are closed. It was never stressed enough in the physical or mathematical literature…
We prove both analytically and numerically that the total angular momentum of a molecular system undergoing adiabatic Born-Oppenheimer dynamics is conserved only when pseudo-magnetic Berry forces are taken into account. This finding sheds…
Quantum mechanics of bending of a nonrelativistic monoenergetic charged particle beam by a dipole magnet is studied in the paraxial approximation. The transfer map for the position and momentum components of a particle of the beam between…
In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…
The motion of a conducting electron in a quantum dot with one or several dislocations in the underlying crystal lattice is considered in the continuum picture, where dislocations are represented by torsion of space. The possible effects of…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
The angular momentum of a classical electromagnetic plane wave of arbitrary extent is predicted to be, on theoretical grounds, exactly zero. However, finite sections of circularly polarized plane waves are found experimentally to carry…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
The orbital magnetic moment is usually associated with the relativistic spin-orbit interaction, but recently it has been shown that noncollinear magnetic structures can also be its driving force. This is important not only for magnetic…
In the context of a growing interdisciplinary interest in the angular momentum of wave fields, the spin-wave case has yet to be fully explored, with the extensively studied notion of spin transport being only part of the broader picture.…
Quark spin and orbital angular momentum in the nucleon are calculated in symmetry-breaking chiral quark model. The results are compared with data and other models.
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…
In this note, we first obtain the decomposition of the non-relativistic field velocity into the classical part (i.e., the velocity w=p/m OF the center-of-mass (CM), and the so-called quantum part (i.e., the velocity V of the motion IN the…
We demonstrate that spin-orbit coupled states are generated in neutral magnetic spin 1/2 particles travelling through an electric field. The quantization axis of the orbital angular momentum is parallel to the electric field, hence both…
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.
In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We integrate the corresponding Hamiltonian equations in…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…