Controlled-scattering resonances in a spherical potential well

Berry phase for a particle in an infinite spherical potential well with moving wall

In this paper we calculate the Berry phase for a wave function of a particle in an infinite spherical potential well with adiabatically varying. In order to do this, we need the solutions of the corresponding Schrödinger equation with a time dependent Hamiltonian. Here, we obtain these solutions for the first time. In addition, we calculate the Berry phase in one dimensional case for an infinit...

Scattering Resonances for a Two-Dimensional Potential Well with a Thick Barrier

This paper is concerned with the scattering resonances of the Schrödinger operator −∆ + VL in R2. The real valued potential VL is a low energy well surrounded by a barrier with finite thickness proportional to L. We are interested in the resonances that are close to the non-degenerate bound state frequencies associated with the potential that has infinitely thick barrier. In particular, it is s...

Resonances of a Potential Well with a Thick Barrier

Abstract. This work is motivated by the desire to develop a method that allows for easy and accurate calculation of complex resonances of a one-dimensional Schrödinger’s equation whose potential is a low-energy well surrounded by a thick barrier. The resonance is calculated as a perturbation of the bound state associated with a barrier of infinite thickness. We show that the corrector to the bo...

A New Theorem Concerning Scattering of Electromagnetic Waves in Multilayered Metamaterial Spherical Structures

The proposed theorem in this paper is indicative of a kind of duality in the propagation of waves in the dual media of and in the spherical structures. Independent of wave frequency, the number of layers, their thickness, and the type of polarization, this theorem holds true in case of any change in any of these conditions. Theorem: Consider a plane wave incident on a multilayered spheric...

Existence of Resonances in Even Dimensional Potential Scattering