Related papers: Garrett approximation revisited
Garrett's approximation for the calculation of bound states energy in square wells is applied in a consistent way. So, one obtains simple formulas for these energies, with errors of about 1% for moderate, and 0.01% for deep wells. The…
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…
Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave…
In this paper, we apply the method of approximate transformation groups proposed by Baikov, Gaziziv and Ibragimov, to compute the first-order approximate symmetry for the Gardner equations with the small parameters. We compute the optimal…
A general class of Newton algorithms on Gra{\ss}mann and Lagrange-Gra{\ss}mann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local quadratic convergence of the algorithm is shown under a suitable condition…
The paper summarizes the parallel session B3 {\em Analytic approximations, perturbation methods, and their applications} of the GR18 conference. The talks in the session reported notably recent advances in black hole perturbations and…
It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish…
This paper revisits quantum corrections to gravity. It was shown previously by other authors that quantum field theories in curved space time provide quadratic curvature forms as quantum corrections to gravity in a conformally flat metric.…
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
Regular generalizations of spherically and axially symmetric metrics and their properties are considered. Newton gravity law generalizations are reduced for null geodesic.
In a recently developed approximation technique for quantum field theory the standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In this…
We examine in detail nonperturbative corrections for low lying energies of a symmetric triple-well potential with non-equivalent vacua, for which there have been disagreement about asymptotic formulas and controversy over the validity of…
A short review of scalar curvature invariants in gravity theories is presented. We introduce how these invariants are constructed and discuss the minimal number of invariants required for a given spacetime. We then discuss applications of…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We introduce a new type of quadrature, known as approximate Gaussian quadrature (AGQ) rules using {\epsilon}-quasiorthogonality, for the approximation of integrals of the form \int f(x)d \alpha(x). The measure {\alpha}(\cdot) can be…
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A…
A thorough analysis of Galilean symmetries for the gravitational well problem on a noncommutative plane is presented. A complete closure of the one-parameter centrally extended Galilean algebra is realised for the model. This implies that…
This manuscript reviews theoretical results and applications related to quadratic forms in Gaussian random variables. It summarizes definitions, canonical representations, exact and approximate distributional results, numerical inversion…
A novel general approximation scheme (NGAS) proposed earlier (ref.2-3) is applied to the problem of the quartic anharmonic (QAHO) and the double-well-oscillator (QDWO) in quantum theory by choosing the infinite square-well-potential in one…