Related papers: An improved semiclassical method with reference po…
A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
In this study, we analyze the bound-state energy spectrum of quark-antiquark systems using the semiclassical WKB approximation. We consider the Cornell potential, which combines a linear confinement term with a Coulombic interaction, and…
We demonstrate how a certain new form of the quantization condition proposed earlier can be used outside the class of potentials for which this form ensures exact spectra. Taking this form as a base we get an improved interpolating…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a…
We show that quasiparticle (QP) energies as calculated in the $GW$ approximation converge to the wrong value using the projector augmented wave (PAW) method, since the overlap integrals between occupied orbitals and high energy, plane wave…
We calculate the critical parameters for some simple quantum wells by means of the Riccati-Pad\'{e} method. The original approach converges reasonably well for nonzero angular-momentum quantum number $l$ but rather too slowly for the s…
The classical WKB method (also known as the WKBJ method, the LG method, or the phase integral method) for solving singularly perturbed linear differential equations has never, as far as we know, been looked at from the structured backward…
Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semi-classical WKB method to first revisit the computation of bound…
We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Pad\'e approximants that are known to provide the best…
Radial wave functions for power-law potentials are approximated with the help of power-law substitution and explicit summation of the leading constituent WKB series. Our approach reproduces the correct behavior of the wave functions at the…
A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand…
Using the generalized coherent states we argue that the path integral formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$ being given by…
In this work, we use rational approximation to improve the accuracy of spectral solutions of differential equations. When working in the vicinity of solutions with singularities, spectral methods may fail their propagated spectral rate of…
Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…
We present a swift walk-through of our recent work that uses machine learning to fit interatomic potentials based on quantum mechanical data. We describe our Gaussian Approximation Potentials (GAP) framework, discussing a variety of…
We derive new approximations for quintessence solutions that are simpler and an order of magnitude more accurate than anything available in the literature, which from an observational perspective \emph{makes numerical calculations…
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…