Scattering through a straight quantum waveguide with combined boundary conditions

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...

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Bibliographic Details
Published in:Journal of mathematical physics 2014-11, Vol.55 (11), p.1
Main Authors: Briet, Ph, Dittrich, J., Soccorsi, E.
Format: Article
Language:English
Subjects:
BOUNDARY CONDITIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIRICHLET PROBLEM
Matching
MATHEMATICAL SOLUTIONS
Mathematics
Physics
Quantum physics
SCATTERING
Spectral Theory
Transition probabilities
TWO-DIMENSIONAL CALCULATIONS
WAVE PACKETS
WAVEGUIDES
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4901547