Mathematica Journal
Volume 10, Issue 1


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T R O T T ' S C O R N E R
Michael Trott


In this Corner, we calculated eigenfunctions belonging to the continuous spectrum of an infinite 2D domain with Dirichlet boundary conditions. Using the mode-matching technique and expansion in eigenfunctions of rectangular and circular domains, we reduced the problem to the numerical evaluation of a few integrals and the calculation of pseudoinverses. Using the expansion coefficients, we calculated the eigenfunctions and the corresponding current densities. The interested reader can continue with changing the ratio of the arm width to the center disk diameter or calculating Bohm trajectories of microparticles instead of the streamlines of the current vector field. Or one could search for localized normalizable eigenfunctions below the beginning of the continuum spectrum using singular value decompositions of the left-hand side matrices (no right-hand side vectors) for states symmetric or antisymmetric with respect to the -axis. Or one could investigate the statistics of the wave function and current values within the center disk [7]. Or one could cut a hole in the center disk and investigate the influence of a Aharanov-Bohm-type magnetic field through this hole [6]. Or...

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