A numerical scheme is described to compute the reflection, absorption, and transmission coefficients of TEm,0 and plane electromagnetic waves propagating in a nonuniform plasma slab. The numerical solutions are in good agreement with theoretical solutions for two different kinds of electron density profiles. The solutions for various electron density profiles will be shown in TEm,0 mode. The me...

Scattering on the PT -symmetric Coulomb potential is studied along a Ushaped trajectory circumventing the origin in the complex x plane from below. This trajectory reflects PT symmetry, sets the appropriate boundary conditions for bound states and also allows the restoration of the correct sign of the energy eigenvalues. Scattering states are composed from the two linearly independent solutions...

While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little work seems to have been put into the complementary problem of establishing rigourous bounds on the exact solutions. We have in mind either bounds on parametric...