Geodesic
Spectrum of three-dimensional landau operator perturbed by a~periodic point potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 2, pp. 283-294

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A study is made of a three-dimensional Schrödinger operator with magnetic field and perturbed by a periodic sum of zero-range potentials. In the case of a rational flux, the explicit form of the decomposition of the resolvent of this operator with respect to the spectrum of irreducible representations of the group of magnetic translations is found. In the case of integer flux, the explicit form of the dispersion laws is found, the spectrum is described, and a qualitative investigation of it is made (in particular, it is established that not more than one gap exists). 
@article{TMF_1995_103_2_a8,
     author = {V. A. Geiler and V. V. Demidov},
     title = {Spectrum of three-dimensional landau operator perturbed by a~periodic point potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {283--294},
     publisher = {mathdoc},
     volume = {103},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a8/}
}
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V. A. Geiler; V. V. Demidov. Spectrum of three-dimensional landau operator perturbed by a~periodic point potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 2, pp. 283-294. http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a8/