Year: 2014
Type: article
Abstract: Scattering through a straight two-dimensional quantum waveguide \documentclass[12pt]{minimal}\begin{document}$\mathbb {R} \times (0,d)$\end{document}R×(0,d) with Dirichlet boundary conditions on \documentclass[12pt]{minimal}\begin{document}$(\mathbb {R}_-^* \times \lbrace y=0 \rbrace ) \cup (\mathbb {R}_+^* \times \lbrace y=d \rbrace )$\end{document}(R−*×{y=0})∪(R+*×{y=d}) and Neumann boundary condition on \documentclass[12pt]{minimal}\begin{document}$(\mathbb {R}_-^* \times \lbrace y=d \rbrace ) \cup (\mathbb {R}_+^* \times \lbrace y=0 \rbrace )$\end{document}(R−*×{y=d})∪(R+*×{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.
Source: Journal of Mathematical Physics
DOI: 10.1063/1.4901547
Authors: Ph. Briet, J. Dittrich, E. Soccorsi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1968785481