The objective of this paper is to construct the accurate (say, 11 decimal places) frequencies quasinormal modes five-dimensional Schwarzschild-Tangherlini black hole using three major techniques: Hill determinant method, continued fractions and WKB-Pad\'e method discuss limitations each. It shown that for massless scalar, gravitational tensor, vector, electromagnetic vector perturbations consid...

Reformulating the instantons in a complex plane for tunneling or transmitting states, we calculate the pair-production rate of charged fermions in a spatially localized electric field, illustrated by the Sauter electric field E0 sech (z/L), and in a temporally localized electric field such as E0 sech (t/T ). The integration of the quadratic part of WKB instanton actions over the frequency and t...

The propagation of dissipationless, hydromagnetic, purely toroidal Alfvén waves in a realistic background three-fluid solar wind with axial symmetry and differential proton-alpha flow is investigated. The short wavelength WKB approximation is not invoked. Instead, the equations that govern the wave transport are derived from standard multi-fluid equations in the five-moment approximation. The A...

The propagation of dissipationless, hydromagnetic, purely toroidal Alfvén waves in a realistic background three-fluid solar wind with axial symmetry and differential proton-alpha flow is investigated. The short wavelength WKB approximation is not invoked. Instead, the equations that govern the wave transport are derived from standard multi-fluid equations in the five-moment approximation. The A...

A recent renewed claim that the instanton method and the WKB method do not lead to identical results in the 1–loop approximation is repudiated. It is pointed out that the WKB method, or its equivalent, yields the instanton result provided the boundary conditions are imposed on wave functions which are properly matched in domains of overlap.

A discrete version of the WKB method is developed and applied to calculate the tunnel splittings between classically degenerate states of spin Hamiltonians. The results for particular model problems are in complete accord with those previously found using instanton methods. The discrete WKB method is more elementary and also yields wavefunctions. 03.65.Sq, 33.20.-t, 75.45.+j Typeset using REVTEX

Higher order simple-pole type operators, that is, higher order linear ordinary differential operators with a large parameter η whose coefficients have simple poles at the origin, are discussed from the viewpoint of the exact WKB analysis. Making use of the technique of microdifferential operators, we clarify the singularity structure of the Borel transform of their WKB solutions.

The paper is devoted to the description of the main geometric and analytic tools of a complex WKB method for adiabatic problem. We illustrate their use by numerous examples. Résumé. L’article est consacré à la description des principaux outils géométriques et analytiques d’une méthode WKB complexe pour des problèmes adiabatiques. Nous illustrons leur utilisation par de nombreux exemples.

We obtain the rigorous WKB expansion to all orders for the radial Kepler problem, using the residue calculus in evaluating the WKB quantization condition in terms of a complex contour integral in the complexified coordinate plane. The procedure yields the exact energy spectrum of this Schrödinger eigenvalue problem and thus resolves the controversies around the so-called ”Langer correction”. Th...