Connecting wave functions at a three-leg junction of one-dimensional channels
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We propose a scheme to connect the wave functions on different one-dimensional branches of a three-leg junction (Y-junction). Our scheme differs from that due to Griffith [Trans. Faraday Soc. 49, 345 (1953)] in the respect that ours can model the difference in the widths of the quasi-one-dimensional channels in different systems. We test our scheme by comparing results from a doubly-connected one-dimensional system and a related quasi-one-dimensional system, and we find a good agreement. Therefore our scheme may be useful in the construction of one-dimensional effective theories out of (multiply-connected) quasi-one-dimensional systems.
6 pages, 4 figures
6 pages, 4 figures