We study the non-relativistic charge-monopole system when the charged particle has a position-dependent mass written as M(r) = m0rw. The angular wave functions are the well-known monopole harmonics, and the radial ones are ordinary Bessel functions which depend on the magnetic and electric charge product as well as on the w parameter. We investigate mappings—approximate and exact—between the charge-monopole system with constant mass and the charge with a position-dependent mass solving the position-dependent mass Schrödinger equation for the mass distribution.
The main purpose of this work is to reproduce a quantum system charge-monopole utilizing position-dependent effective mass (PDM) system in the nonrelativistic regime via the Pauli equation. In this case, we substitute the exact charge-monopole wavefunction into the free PDM Pauli equation and then solve it for the mass distribution considering a radial dependence only, i.e., M = M(r). The resulting equations are nonlinear, and in such cases, we were able to numerically solve them, fixing θ0 and considering specific values of μ and m satisfying a given condition. The mapping was studied for eigenvalues starting from the minimal value j = μ − 1/2.
The primary purpose of this work is to reproduce the scenario composed of a charge-dyon system utilizing position-dependent effective mass (PDM) background in the non-relativistic and in the relativistic regimes. In the non-relativistic case we substitute the exact charge-dyon eigenfunction into PDM Schrödinger equation, in the Zhu-Kroemer parametrization, and then solve it for the mass distribution considering M = M(r). Analogously, in the relativistic case we study the Klein-Gordon equation for a position-dependent mass, and in this case, we are able to analytically solve the equation for M = M(r,θ).
We study the non-relativistic quantum mechanical scattering of a plane wave by a shield barrier and an elliptical aperture modeled as Dirac delta functions running along a coordinate surface of the sphero-conal coordinate system. The scattering problem is formulated via Lippmann-Schwinger (LS) equation in the position representation. In order to solve the LS equation, we first calculate the free Green's function of the problem and obtain its bilinear expansion in terms of the eigenfunctions of the scalar Helmholtz equation—which are products of spherical Bessel (or first kind Hankel) functions and Lamé polynomials. Such bilinear expansion allows us to obtain an integral equation with a separable kernel and solve the scattering problem. Then, we calculate the wavefunctions in the internal and external domains and the scattering amplitudes.
We investigate the scattering of a plane wave in the hyperbolic plane. We formulate the problem in terms of the Lippmann-Schwinger equation and solve it exactly for barriers modeled as Dirac delta functions running along: (i) N − horizontal lines in the Poincaré upper half-plane; (ii) N − concentric circles centered at the origin; and, (iii) a hypercircle in the Poincaré disk.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.