Classical properties of quantum scattering

Władysław Żakowicz

Quantum elastic potential scattering of a particle is re-examined taking into account exact solutions of the corresponding Schrödinger equation. In addition to the scattering of stationary plane waves and stationary finite-width wave beams, nonstationary wave packets having finite duration times are studied and some corresponding examples are presented. The role of interference between the scattered wave and the advancing incident beam is studied. Several two-dimensional scattering problems, involving axially symmetric, generic examples of nonuniform attractive and repulsive potentials, are discussed in more detail. This discussion concentrates on finding proper conditions when the solutions of the Schrödinger equation may resemble the corresponding solutions of the classical Newton equation. Examples are shown where such similarities occur.

J. Phys. A vol. 36, 4445-4464 (2003)

Interaction of an atom with a small dispersive and absorptive dielectric body

The paper analyzes the interaction of an atomic system with a quantum damped harmonic oscillator. Such an oscillator is the building block in the recently proposed models of bulk dielectrics and may also serve as a simple model of a small dielectric body. Dispersion and losses are taken into account by assuming the oscillator to be coupled to a zero-temperature reservoir consisting of an infinite system of other harmonic oscillators. The Green’s function of the atomic system is calculated perturbatively when coupled to the bath. The self-energy of the atomic electron is obtained by the partial resummation of perturbation diagrams, and thus energy-level shifts of both ground and excited states of the atom due to the presence of the oscillator are determined. Corrections to the decay rates are also obtained and analyzed as functions of the distance of the atom from the oscillator, and of the coupling of the oscillator to the reservoir.

Phys. Rev. A vol. 67, 063816-1-14 (2003) Claudia Eberlein and Maciej Janowicz