Related papers: Three-dimensional transformation for rotating coor…
The purpose of this paper is to show that the mathematical treatment of three dimensional rotations can be simplified, and its geometrical understanding improved, by using the Rodrigues' vector representation. We present a novel geometrical…
A novel effect of rotation in the optical image of structures in an opaque screen is presented. Theoretical calculations and experimental validation are presented. The features and the conditions of this effect are discussed.
A method is presented, which can generate solutions of the Hermitian theory of relativity from known solutions of the general theory of relativity, when the latter depend on three co-ordinates and are invariant under reversal of the fourth…
General relativistic quantum dynamics of twisted (vortex) Dirac particles is constructed. The Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived for a twisted relativistic electron in arbitrary electric…
The derivation of the transformations between inertial frames made by Mansouri and Sexl is generalised to three dimensions for an arbitrary direction of the velocity. Assuming lenght contraction and time dilation to have their relativistic…
In engineering practice one often encounters planar problems, where the corresponding vector space of forces, velocities or (infinitesimal) displacements is three dimensional. This paper shows how these spaces can be factorized, such that…
In this paper, we give the solution of the three dimensional quantum stationary Hamilton-Jacobi Equation (3D-QSHJE) for a general form of the potential. We present the quantum coordinates transformation with which the 3D-QSHJE takes its…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
In this work we apply the formalism developed in [M. Lepers \emph{et al}., Phys. Rev. A \textbf{77}, 043628 (2008)] to different initial conditions corresponding to systems usually met in real-life experiments, and calculate the observable…
Numerical relativity has made big strides over the last decade. A number of problems that have plagued the field for years have now been mostly solved. This progress has transformed numerical relativity into a powerful tool to explore…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
Modern applications of Covariant Density Functional Theory (CDFT) are discussed. First we show a systematic investigation of fission barriers in actinide nuclei within constraint relativistic mean field theory allowing for triaxial…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
The classical and the quantum motion of a massive body in the rotating tube is considered. Photon is included. The spin motion described by the Bargmann-Michel-Telegdi equation is considered in the rotation tube and rotating system.
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…
We analyze a variety of Weyl invariant dynamical problems in three dimensions.
Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of…
A summary of the known results on integration theory on the space of connections modulo gauge transformations is presented and its significance to quantum theories of gauge fields and gravity is discussed. The emphasis is on the underlying…
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum…
We present a general theory of spin-to-orbital angular momentum (AM) conversion of light in focusing, scattering, and imaging optical systems. Our theory employs universal geometric transformations of nonparaxial optical fields in such…