ﻻ يوجد ملخص باللغة العربية
The motion of a particle in the field of dispiration (due to a wedge disclination and a screw dislocation) is studied by path integration. By gauging $SO(2) otimes T(1)$, first, we derive the metric, curvature, and torsion of the medium of dispiration. Then we carry out explicitly path integration for the propagator of a particle moving in the non-Euclidean medium under the influence of a scalar potential and a vector potential. We obtain also the winding number representation of the propagator by taking the non-trivial topological structure of the medium into account. We extract the energy spectrum and the eigenfunctions from the propagator. Finally we make some remarks for special cases. Particularly, paying attention to the difference between the result of the path integration and the solution of Schrodingers equation in the case of disclination, we suggest that Schrodinger equation may have to be modified by a curvature term.
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can
Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charg
We study space-inhomogeneous quantum walks (QWs) on the integer lattice which we assign three different coin matrices to the positive part, the negative part, and the origin, respectively. We call them two-phase QWs with one defect. They cover one-de
In addition to the well known case of spherical coordinates the hydrogen atom separates in three further coordinate systems. Separating in a particular coordinate system defines a system of three commuting operators. We show that the joint spectrum o
In [7] we proposed a non-generational conjectural derivation of all first class constraints (involving, only, variables compatible with canonical Poisson brackets) for realistic gauge (singular) field theories; and we verified the conjecture in cases