Wigner Not the ‘W’ in WKB

Wigner Functions versus WKB-Methods

We consider the Cauchy-problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of high-frequency asymptotics of such models is reviewed, in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods, leading to ”multi-valued” solutions of Hamilton-Jacobi equations. Using Wigner measures we present an...

Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics

We consider the Cauchy problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of the high-frequency asymptotics of such models is reviewed, in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods. Using Wigner measures we present an alternative approach to such asymptotic problems. We first di...

Light scattering by cubical particle in the WKB approximation

In this work, we determined the analytical expressions of the form factor of a cubical particle in the WKB approximation. We adapted some variables (size parameter, refractive index, the scattering angle) and found the form factor in the approximation of Rayleigh-Gans-Debye (RGD), Anomalous Diffraction (AD), and determined the efficiency factor of the extinction. Finally, to illustrate our form...

Accuracy of the WKB

Arbitrary tip orientation in STM simulations: 3D WKB theory and application to W(110).

We extend the orbital-dependent electron tunnelling model implemented within the three-dimensional (3D) Wentzel-Kramers-Brillouin (WKB) atom-superposition approach for simulating scanning tunnelling microscopy (STM) by including arbitrary tip orientations. The orientation of the tip is characterized by a local coordinate system centred on the tip apex atom obtained by a rotation with respect to...