Related papers: Monopole Vector Spherical Harmonics
The quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to a harmonic and a linear confining potentials is investigated. It is shown that the interaction between the magnetic…
The derivation of spherical harmonics is the same in nearly every quantum mechanics textbook and classroom. It is found to be difficult to follow, hard to understand, and challenging to reproduce by most students. In this work, we show how…
We show that for massless helicity $h$ particles, the angular momentum eigenstates are given in an appropriate coordinate system by the spin-weighted spherical harmonics ${_{-h}Y_{jm}}$ of spin-weight $-h$. In particular, these are…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
The possibility of the magnetic monopole decay in the constant electric field is investigated and the exponential factor in the probability is obtained. Corrections due to Coulomb interaction are calculated. The relation between masses of…
We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of…
We prove Lieb-Thirring inequalities for Schr\"odinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength…
We study angular momentum of the electron stored in its electric and magnetic fields. We use for this purpose quantum electrodynamics in the covariant gauge. We show that a finite one-loop result for such angular momentum can be obtained…
In this note we consider high energy eigenfunctions of the harmonic oscillator in $\mathbb{R}^d$ and prove that any invariant measure on the energy surface can be written as a weak limit of eigenfunctions.
Localized photon states have non-zero angular momentum that varies with the non-unique choice of a transverse basis and is changed by gauge transformations of the geometric vector potential $\mathbf{a}$. The position operator must depend on…
It is well-known that an electric charge under a uniform magnetic field has a bidimensional motion if its initial position and velocity are perpendicular to this magnetic field. Although some constants of motion, as the energy and angular…
A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the…
In this paper we follow the Schwinger approach for angular momentum but with the polar basis of harmonic oscillator as a starting point. We derive by a new method two analytic expressions of the elements of passage matrix from the double…
Following the recent studies of the trickiness in spin and orbital angular momentum of the vector gauge fields, we perform here a parallel analysis for the tensor gauge field, which has certain relation to gravitation. Similarly to the…
The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn into self-adjoint the spatial portion of the wave operator…
We consider the vector functions in a domain homeomorphic to a spherical layer bounded by twice continuously differentiable surfaces. Additional restrictions are imposed on the domain, which allow to conduct proofs using simple methods. On…
As a submanifold is embedded into higher dimensional flat space, quantum mechanics gives various embedding quantities, e.g., the geometric momentum and geometric potential, etc. For a particle moving on a two-dimensional sphere or a free…
In experiments the distinction between spin-torque and Oersted-field driven magnetization dynamics is still an open problem. Here, the gyroscopic motion of current- and field-driven magnetic vortices in small thin-film elements is…
Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic…
We analyze the torque applied to a rotating magnetized sphere in a vacuum. It is shown that for the correct determination of one of the torque's component the angular momentum of the electromagnetic field within the body should be taken…