The Classical-to-Semiclassical Connection

John A. Adam

John Adam

This chapter discusses the connection between the classical and semiclassical domains of scattering. Scattering phenomena may be described via three regimes: the scattering of waves by objects with small, large, or comparable sizes with the wavelength of the incident (plane wave) radiation. All three regions can be related to three domains: the classical domain (geometrical optics, particle and particle/ray-like trajectories); the wave domain (physical optics, acoustic and electromagnetic waves, quantum mechanics); and the semiclassical domain (the vast intermediate region between the first and second domain). The chapter first provides an overview of classical and semiclassical scattering domains before beginning with an analysis of the semiclassical formulation. It also considers the radial equation, scattering by a one-dimensional potential barrier, and the radially symmetric problem. Solutions for phase shifts and the potential well are presented.

Cécile DeWitt-Morette

ARTUR K. EKERT, P. L. Knight

We discuss the relationship between fully quantized and semiclassical approaches to input-output theory that connect asymptotically free fields prior to and following interactions that we describe in terms of canonical transformations. We demonstrate the utility of the Wigner function in describing the connection between input and output fields, and show how it is particularly well suited to describe many quantum-optical systems in terms of positive quasiprobability permitting classical stochastic simulation.

Christian Grosche, Frank Steiner

Е. А. Соловьев