The X-ray problem revisited

Asymptotic Electromagnetic Fields in Non-relativistic QED: the Problem of Existence Revisited

This paper is devoted to the scattering of photons at electrons in models of non-relativistic quantum mechanical particles coupled minimally to the soft modes of the quantized electromagnetic field. We prove existence of scattering states involving an arbitrary number of asymptotic photons of arbitrarily high energy. Previously, upper bounds on the photon energies seemed necessary in the case of $n>1$ asymptotic photons and non-confined, non-relativistic charged particles.

The Malyuzhinets-Popov diffraction problem revisited

In this paper, the high-frequency diffraction of a plane wave incident along a planar boundary turning into a smooth convex contour, so that the curvature undergoes a jump, is asymptotically analysed. An approach modifying the Fock parabolic-equation method is developed. Asymptotic formulas for the wavefield in the illuminated area, shadow, and the penumbra are derived. The penumbral field is characterized by novel and previously unseen special functions that resemble Fock's integrals.

Wooding问题再审视

The Wooding problem revisited

研究重新审视Wooding问题，考虑边界热传导不完美情况，分析流体在多孔介质中的对流不稳定性，探讨两种不同Rayleigh数定义及其在临界稳定性下的表现。

Delta potentials revisited via Fourier transform

The problem of bound states in delta potentials is revisited by means of Fourier transform approach. The problem in a simple delta potential sums up to solve an algebraic equation of degree one for the Fourier transform of the eigenfunction and the problem for more than one delta function also reveals itself to be a simple matter. Quite differently from direct methods, no knowledge about the jump discontinuity of the first derivative of the eigenfunction is required to determine the solution of the problem.

The Damped String Problem Revisited

We revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it, employing methods familiar from supersymmetric quantum mechanics. We also derive completeness and Riesz basis results (with parentheses) for the associated root functions under less smoothness assumptions on the coefficients than usual, using operator theoretic methods (rather than detailed eigenvalue and root function asymptotics) only.

Pseudotensor problem of gravitational energy-momentum and Noether's theorem revisited

Based on a general variational principle, Noether's theorem is revisited. It is shown that the so called pseudotensor problem of the gravitational energy-momentum is a result of mis-reading Noether's theorem, and in fact, all the Noether's conserved quantities are scalars. It is also shown, by using a counter-example, that the non-localizability of gravitational energy-momentum can not be attributed to the equivalence principle. As a direct consequence of variational principle, a generalized Hamilton-Jacobi equation for the Hamilton's principal functional is obtained.