Scattering through a straight quantum waveguide with combined boundary conditions

Overview & Synopsis

Scattering through a straight two-dimensional quantum waveguide R × (0, d) with Dirichlet boundary conditions on (R * − × {y = 0}) ∪ (R * + × {y = d}) and Neumann boundary condition on (R * − × {y = d}) ∪ (R * + × {y = 0}) is considered using sta-tionary 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.