A WKB formula for echoes

A Haar wavelets approach to Stirling's formula

This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.

Accuracy of the WKB

WKB approximation for inflationary cosmological perturbations

A new method for predicting inflationary cosmological perturbations, based on the Wentzel-KramersBrillouin ~WKB! approximation, is presented. A general expression for the WKB scalar and tensor power spectra is derived. The main advantage of the new scheme of approximation is that it is valid even if the slow-roll conditions are violated. The method is applied to power-law inflation, which allow...

I . Search for Light Echoes

We have used FORS1 at the ESO VLT to search for light echoes in imaging polarimetry from four historical supernovæ in the face-on nearby spiral galaxy M83 (NGC 5236). No echoes were detected around our targets (SN 1923A, SN 1945B, SN 1950B and SN 1957D). This implies that the interstellar medium in their environs is rather tenuous (a few particles per cm), possibly as a result of previous super...

WKB for coupled equations and virial coefficientsa)

Using semiclassical expressions for eigenphase shifts and bound state energies arising from WKB approximations to the solutions of coupled equations. we show that quantum mechanical formulas for the third virial coefficient (restricted to positive potentials) and for the second virial cofficient (with anisotropic interactions) lead to the known classical results when Ii goes to zero. The proced...