Scattering through a straight quantum waveguide with combined boundary conditions

TL;DR

This paper analyzes quantum waveguide scattering with mixed boundary conditions, establishing solution existence, relating stationary scattering theory to wave packet dynamics, and providing numerical transition probability results.

Contribution

It introduces a rigorous proof of solution existence for a quantum waveguide with combined boundary conditions and connects stationary scattering theory to wave packet motion.

Findings

Existence of matching conditions solution proved

Stationary scattering theory related to wave packet dynamics

Numerical transition probabilities demonstrated

Abstract

Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is considered using stationary scattering theory. The existence of a matching conditions solution at x=0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown.