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On the spectrum of Schrödinger operators with a finitely supported potential on the -regular tree

✍ Scribed by Kazunori Ando; Yusuke Higuchi

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 220 KB
Volume: 431
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.06.033

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✦ Synopsis

We study the spectrum of Schrödinger operators with a uniform potential on the lth shell of the d-regular tree. As a result, we show the relationship between the spectral structure and the intensities of the potential. Furthermore we completely determine the discrete eigenvalues with their multiplicities. In addition we give some examples.

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