Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010Spectral problems. Issue dedicated to the memory of M. Birman
|Page(s)||175 - 197|
|Published online||12 May 2010|
Schrödinger Operator on the Zigzag Half-Nanotube in Magnetic Field
Institute of Mathematics and Physics, Aberystwyth Univ., Penglais, Ceredigion, SY23 3BZ, UK
2 School of Mathematics, Cardiff Univ., Senghennydd Road, Cardiff, CF24 4AG, UK
* Corresponding author. E-mail:
We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.
Mathematics Subject Classification: 47B36 / 81U15 / 47N50 / 81V99
Key words: nanotubes / Jacobi operator / periodic / finite support perturbation / resonances
© EDP Sciences, 2010
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