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Journal of Physics A: Mathematical and General






We describe the bound state and scattering properties of a quantum mechanical particle in a scalar N-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy levels for the special case of N identical prongs exhibit an alternating pattern of non-degeneracy and (N−1) fold degeneracy. It is shown that the techniques of supersymmetric quantum mechanics can be used to generate new solutions. Solutions for prongs of arbitrary lengths are developed. Discussions of tunneling in N-well potentials and of scattering for piecewise constant potentials are given. Since our treatment is for general values of N, the results can be studied in the large N limit. A somewhat surprising result is that a free particle incident on an N-prong vertex undergoes continuously increased backscattering as the number of prongs is increased.


Author Posting. © Gangopadhyaya et al., 1995. This is the author's version of the work. It is posted here by permission of the authors for personal use, not for redistribution. The definitive version was published in Journal of Physics A: Mathematical and General, Volume 28, Issue 18, 1995.

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