Related papers: Exact method for locating potential resonances and…
A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…
We provide some explicit examples wherein the Schr\"odinger equation for the Morse potential remains exactly solvable in a position-dependent mass background. Furthermore, we show how in such a context, the map from the full line $(-…
We present an eikonal-based approach that is capable of finding a continuous globally optimal trajectory for an aircraft in a stationary wind field. This minimizes emissions and fuel consumption. If the destination is close to a cut locus…
We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures…
A new method of momentum measurement of charged particles through Multiple Coulomb Scattering (MCS) in the OPERA lead emulsion target is presented. It is based on precise measurements of track angular deviations performed thanks to the very…
A very simple method is devised to derive a (strictly) isospectral extension of the Morse potential. Furthermore, point canonical transformations are used to transform the latter into quasi-exactly solvable extensions of the radial…
A simple and very accurate method to approximate a function with a finite number of discontinuities is presented. This method relies on hyperbolic tangent functions of rational arguments as connecting functions at the discontinuities, each…
Analytical expressions are derived for classical trajectories in repulsive Coulomb plus multi-step attractive potentials. Thereafter the closed form expressions are obtained for classical deflection functions. The expressions are expected…
We study the problem of a particle hopping on the Bethe lattice in the presence of a Coulomb potential. We obtain an exact solution to the particle's Green's function along with the full energy spectrum. In addition, we present a mapping of…
The available R-matrix parametrization of experimental data on the excitation functions for the elastic and inelastic p-Be7 scattering at the collision energies up to 3.4 MeV is used to generate the corresponding partial-wave cross sections…
The Lagrange-mesh method is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature. Although this method provides accurate results in many problems with small number of mesh…
We investigate rigidity phenomena in one-dimensional point processes. We show that the existence of an $L^1$ transport map from a stationary lattice or the Lebesgue measure to a point process is sufficient to guarantee the properties of…
An analytical form has been derived using Ostrogradski's integration method for the interaction between two thin rods of finite lengths in arbitrary relative configurations in a 3-dimensional space, each treated as a line of material points…
We investigate the effect of local Coulomb correlations on electronic transport through a variety of coupled quantum dot systems connected to Fermi liquid leads. We use a newly developed functional renormalization group scheme to compute…
Analytic solutions of the Regge-Wheeler equation are presented in the form of series of hypergeometric functions and Coulomb wave functions which have different regions of convergence. Relations between these solutions are established. The…
For a two-dimensional quantum mechanical problem, we obtain a generalized power-series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similarly to the standard effective range…
In this work we find analytical solutions to the null geodesics around a black hole in the conformal Weyl gravity. Exact expressions for the horizons are found, and they depend on the cosmological constant and the coupling constants of the…
Relativistic formalism of Green's functions is dicussed in QCD and QED,where the relativistic Green's functions are constructed using the Schwinger proper time formalism and the Fock-Feynman-Schwinger method.As a result a simple and exact…
The well-known Cornell quark-antiquark potential in momentum space contains singularities both in its one-gluon-exchange (OGE) and linear confining parts, which prevents a direct use of the convenient Nystr\"om method to solve the…
We consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass$M$, described by the Klein-Fock-Gordon equation with equal scalar $S(\vec{r})$ and vector $V(\vec{r})$ Coulomb plus ring-shaped…