Related papers: Polynomial potentials determined from the energy s…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
Semiclassical quantization rules and numerical calculations are applied to study polariton modes of materials whose permittivity tensor has principal values of opposite sign (so-called hyperbolic materials). The spectra of volume- and…
An improved formulation of the one-step model of photoemission from crystal surfaces is proposed which overcomes different limitations of the original theory. Considering the results of an electronic-structure calculation, the electronic…
We provide a mathematical analysis of appearance of the concentrations (as Dirac masses) of the solution to a Fokker-Planck system with asymmetric potentials. This problem has been proposed as a model to describe motor proteins moving along…
We derive an expression for the local transverse polarization of a boost-invariant expanding system of massive particles, which involves a set of dynamical spin moments. Starting from spin kinetic theory, we obtain a closed set of equations…
We have studied the path integral solution of a system of particle moving in certain class of non-central potential without using Kustannheimo-Stiefel transformation. The Hamiltonian of the system has been converted to a separable…
In previous publications, we illustrated the effectiveness of the method of the inhomogeneous differential equation in calculating the electric polarizability in the one-dimensional problem. In this paper we extend our effort to apply the…
We study the generalized quantum isotonic oscillator Hamiltonian given by H=-d^2/dr^2+l(l+1)/r^2+w^2r^2+2g(r^2-a^2)/(r^2+a^2)^2, g>0. Two approaches are explored. A method for finding the quasi-polynomial solutions is presented, and…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some…
By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
The shift of atomic energy levels due to hadronic vacuum polarization is evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen. A parametric hadronic polarization function obtained from experimental cross sections…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of…
We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…
We demonstrate a polynomial approach to express the decision version of the directed Hamiltonian Cycle Problem (HCP), which is NP-Complete, as the Solvability of a Polynomial Equation with a constant number of variables, within a bounded…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…