Related papers: Special rectangular (double-well and hole) potenti…
We consider the self-energy and the self-force for an electrically charged particle at rest in the wormhole space-time. We develop general approach and apply it to two specific profiles of the wormhole throat with singular and with smooth…
We obtain an exact solution of the 1D Dirac equation for a square well potential of depth greater then twice the particle's mass. The energy spectrum formula in the Klein zone is surprisingly very simple and independent of the depth of the…
In light of some recent experiments on quasi two-dimensional (2D) turbulent channel flow we provide here a model of the ideal case, for the sake of comparison. The ideal 2D channel flow differs from its 3D counterpart by having a second…
We investigate various properties of extremal dyonic static black holes in Einstein-Maxwell-Dilaton theory. Using the fact that the long-range force between two identical extremal black holes always vanishes, we obtain a simple first-order…
We show that in presence of a cosmological constant or, more generally, of a scalar potential, there can exist actually more possibilities for the horizon geometry of a four-dimensional black hole than the hitherto known spherical,…
It is an interesting open problem whether two non-extremal rotating and electrically charged black holes can be in physical equilibrium, which might be possible due to a balance between the gravitational attraction and the spin-spin and…
A nontrivial scalar field configuration of vanishing energy-momentum is reported. These matter configurations have no influence on the metric and therefore they are not be "detected" gravitationally. This phenomenon occurs for a…
Different features of a potential in the form of a Gaussian well have been discussed extensively. Although the details of the calculation are involved, the general approach uses a variational method and WKB approximation, techniques which…
On the basis of two requirements: the avoidance of the curvature singularity and the Maxwell theory as the weak field limit of the nonlinear electrodynamics, we find two restricted conditions on the metric function of $(2+1)$-dimensional…
In higher dimensional gauge theory, we need energies with higher power terms of field strength in order to realize point-wise monopoles. We consider new models with higher power terms of field strength and extraordinary kinetic term of…
We use the discrete approach to solve the Schr\"odinger as well as the Bloch equations for a free particle and the quantum gas of free particles embedded in an infinite quantum well with the finite width. We obtain the expressions of energy…
Standard power series are used to construct and analyze angular and radial spheroidal functions, which are necessary for solving boundary value problems for Helmholtz equation in a spheroid. With an advanced approach the low-lying energy…
Gate-defined quantum dots define an attractive platform for quantum computation and have been used to confine individual charges in a planar array. Here, we demonstrate control over vertical double quantum dots confined in a double quantum…
The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution. The 2+1 black hole -characterized by mass, angular momentum and charge, defined by flux integrals at…
We utilize the amenability of the Fermi-type potential profile in Schr{\"o}dinger equation to construct a symmetric one dimensional well as $V(x){=}{-}U_n/[1+\exp[(|x|{-}a)/b]], ~ U_n{=}V_n[1+\exp[-a/b]]$. We define $\alpha=a/b, ~\beta_n…
All two-dimensional Schr\"{o}dinger equations with symmetric potentials \break $(V_a(\rho)=-a^2g_a \rho ^{2(a-1)/2} {with} \rho=\sqrt{x^2+y^2} {and} a\not=0)$ is shown to have zero energy states contained in conjugate spaces of Gel'fand…
We study the Gibbs equilibrium of a classical 2D Coulomb gas in the determinantal case = 2. The external potential is the sum of a quadratic term and the potential generated by individual charges pinned in several extended groups. This…
The Fourier component of the potential energy of interaction of an atom with an atom is represented as a polynomial of the fourth degree from the atomic form factor. A numerical calculation was performed for the atomic form factor in the…
The surprising divergence of the expectation value $<\!p^6\!>$ for the square well potential is known. Here, we prove and demonstrate the divergence of $<\!p^6\!>$ in potential wells which have a finite jump discontinuity; apart from the…
The Gross-Pitaevskii equation is solved by analytic methods for an external double-well potential that is an infinite square well plus a $\delta$-function central barrier. We find solutions that have the symmetry of the non-interacting…