Related papers: Algorithms of the Potential Field Calculation in a…
The notion that the electromagnetic field is quantised is usually inferred from observations such as the photoelectric effect and the black-body spectrum. However accounts of the quantisation of this field are usually mathematically…
A program has been designed for accurately generating a potential magnetic field on a staggered grid by extrapolating the magnetic field normal to the photospheric surface. The code first calculates a magnetic potential using the Green's…
A method for taking into account the long-range potential of atoms in the framework of the hard-sphere model is proposed. It is shown that thermodynamic quantities can be represented as a sum of three contribution: that of an ideal gas, the…
The main purpose of this paper is to demonstrate and illustrate, once again, the potency of the variational technique as an approximation procedure for the quantization of quantum mechanical systems. By choosing particle-in-a-box…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
Without our ability to model and manipulate the band structure of semiconducting materials, the modern digital computer would be impractically large, hot, and expensive. In the undergraduate QM curriculum, we studied the effect of spatially…
We compute the photon creation inside a perfectly conducting, three dimensional oscillating cavity, taking the polarization of the electromagnetic field into account. As the boundary conditions for this field are both of Dirichlet and…
The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us…
A Hamiltonian analysis of models given by a three-form field with a generic potential coupled to general relativity in four dimensions is performed. This kind of fields are naturally present in string theory and cosmological scenarios. In…
The finite-element analysis of three-dimensional magnetostatic problems in terms of magnetic vector potential has proven to be one of the most efficient tools capable of providing the excellent quality results but becoming computationally…
We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced…
In a model of nonlinear system of three scalar fields the problem on dynamics of a massive particle moving in effective potential provided by two relativistic fields is solving. The potentials for these fields are chosen in the form of…
We consider the 3-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated in the upper…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of…
The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a…
Three mechanisms of capacitance enhance-ment by a magnetic field have been analyz-ed. Through semiclassical description of charge movement under a magnetic field, it can be shown that the charge density gradient, a term coupled with…
We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the…
A recently developed three-dimensional Faddeev integral equations for three-nucleon bound state with two-nucleon interactions have been solved in momentum space for Bonn-B potential.