Abstract
We show that the negative part of the spectrum of the three-dimensional Schrödinger operator with periodic point interactions with a finite number n of centers in each periodic cell consists of, at most, n bands. Furthermore, we show that if one removes the interaction at some arbitrary points the negative part of the spectrum is contained within the lower and upper edge of the negative part of the spectrum of the original operator. More detailed properties of the spectrum in the case n=2 or 3 are also given.
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Supported in part by the Norwegian Research Council for Science and the Humanities under the project Matematisk Seminar, Oslo'.
On leave of absence from Istituto di Fisica GNFM, Universita di Roma, Italy.
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Krohn, R.H., Holden, H. & Martinelli, F. The spectrum of defect periodic point interactions. Letters in Mathematical Physics 7, 221–228 (1983). https://doi.org/10.1007/BF00400437
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DOI: https://doi.org/10.1007/BF00400437