Related papers: Spherical harmonics for fractional quantum numbers…
In this paper we analyze the relativistic quantum motion of charged spin-0 and spin-1/2 particles in the presence of a uniform magnetic field and scalar potentials in the cosmic string spacetime. In order to develop this analysis, we assume…
Despite conventional wisdom that spin-1/2 systems have no classical analog, we introduce a set of classical coupled oscillators with solutions that exactly map onto the dynamics of an unmeasured electron spin state in an arbitrary,…
The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes…
Motivated by the conduction properties of graphene discovered and studied in the last decades, we consider the quantum dynamics of a massless, charged, spin 1/2 relativistic particle in three dimensional space-time, in the presence of an…
It is shown, that the requirement of invariance under spatial rotations reveales an intrinsic fractional extended translation-rotation-like property for particles described with the fractional Schroedinger equation, which we call fractional…
Light-baryon resonances with u,d, and s quarks only can be classified using the non-relativistic quark model. When we assign to baryon resonances with total angular momenta J intrinsic orbital angular momenta L and spin S we make the…
The angular wave functions for a hydrogen atom are well known to be spherical harmonics, and are obtained as the solutions of a partial differential equation. However, the differential operator is given by the Casimir operator of the…
The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…
As an elementary particle the electron carries spin \hbar/2 and charge e. When binding to the atomic nucleus it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies (e.g., s, p or d).…
A relativistic particle in an attractive Coulomb field as well as a static and spherically symmetric gravitational field is studied. The gravitational field is treated perturbatively and the energy levels are obtained for both spin 0…
This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, we provide an explicit derivation for the other two…
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…
Quantum hydrodynamic (QHD) model of charged spin-1/2 particles contains physical quantities defined for all particles of a species including particles with spin-up and with spin-down. Different population of states with different spin…
We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) $\Omega_{\kappa\mu}(\mathbf{n})$ used in relativistic atomic, molecular, and solid state…
Spin-1/2 particles can be used to study inertial and gravitational effects by means of interferometers, particle accelerators, and ultimately quantum systems. These studies require, in general, knowledge of the Hamiltonian and of the…
We describe relativistic particles with spin as points moving in phase space $X=T^* R^{1,3}\times C^2_L\times C^2_R$, where $T^* R^{1,3}=R^{1,3}\times R^{1,3}$ is the space of coordinates and momenta, and $C^2_L$ and $C^2_R$ are the spaces…
In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid…
By carefully considering a family of wave functions for Skyrmions in simple quantum Hall states, whose members are labelled by a non-negative integer and which properly generalizes the traditional Laughlin quasiparticle, we argue that the…
A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary…
In this paper, we propose a method to construct the decay amplitudes in the orbital ($L$) and spin ($S$) coupling scheme for particles with arbitrary spins. For the $1\to 2$ decay with only massive particles involved, the angular dependence…