Related papers: A Note on Derivation of Rutherford Formula within …
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
The Born approximation of a potential in the context of the Calder\'on inverse problem is an object that can be formally defined in terms of spectral data of the Dirichlet-to-Neumann map of the corresponding Schr\"odinger operator. In this…
Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…
In this work we illustrate a number of properties of the Born approximation in the three-dimensional Calder\'on inverse conductivity problem by numerical experiments. The results are based on an explicit representation formula for the Born…
The Born approximation (Born 1926 Z.Phys.38.802) is a fundamental result in physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. As was done by previous authors (Ge et al 2014 New J.…
The first and second Born approximation are studied with the path integral representation for $ {\cal T} $ matrix. The $ {\cal T}$ matrix is calculated for Woods-Saxon potential scattering. To make corresponding integrals solvable…
Derivations of Borns Rule are of interest because they tell us what's connected to what in quantum mechanics if we ever need to change or modify it.
It has been known for some time that, for nonrelativistic Coulomb scattering, the terms in the Born series of second and higher order diverge when using the standard method of calculation. In this paper we take the matrix elements between…
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
We discuss three ways of obtaining the Born approximations for Coulomb scattering: The standard way, making use of a convergence factor ("screening"), Oppenheimer's way using cylindrical (instead of spherical) coordinates, and finally…
The RSE Born Approximation is a new scattering formula in Physics, it allows the calculation of strong scattering at all frequencies via the Fourier transform of the scattering potential and Resonant-states. In this paper I apply the RSE…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
Uniqueness and reconstruction in the three-dimensional Calder\'on inverse conductivity problem can be reduced to the study of the inverse boundary problem for Schr\"odinger operators $-\Delta +q $. We study the Born approximation of $q$ in…
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
The error term in the approximate functional equation for exponential sums involving the divisor function will be improved under certain conditions for the parameters of the approximate functional equation.