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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 1983, Volume 23, Pages 3–32 (Mi intd67)  

This article is cited in 26 scientific papers (total in 26 papers)

Two-dimensional Schrödinger operators in periodic fields

S. P. Novikov


Abstract: A class of problems connected with the description of the motion of an attracted quantum particle in possibly time-dependent, periodic, external fields is studied on the basis of a development of the method of the inverse problem.

Full text: PDF file (1616 kB)

English version:
Journal of Soviet Mathematics, 1985, 28:1, 1–20

Bibliographic databases:

UDC: 517.957+512.7

Citation: S. P. Novikov, “Two-dimensional Schrödinger operators in periodic fields”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 23, VINITI, Moscow, 1983, 3–32; J. Soviet Math., 28:1 (1985), 1–20

Citation in format AMSBIB
\Bibitem{Nov83}
\by S.~P.~Novikov
\paper Two-dimensional Schr\"odinger operators in periodic fields
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat.
\yr 1983
\vol 23
\pages 3--32
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd67}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=734312}
\zmath{https://zbmath.org/?q=an:0564.35083}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 28
\issue 1
\pages 1--20
\crossref{https://doi.org/10.1007/BF02104894}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Zorich, “A problem of Novikov on the semiclassical motion of an electron in a uniform almost rational magnetic field”, Russian Math. Surveys, 39:5 (1984), 287–288  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. M. Krichever, “The laplace method, algebraic curves, and nonlinear equations”, Funct. Anal. Appl., 18:3 (1984), 210–223  mathnet  crossref  mathscinet  zmath  isi
    3. P. G. Grinevich, “Vector rank of commuting matrix differential operators. Proof of S. P. Novikov's criterion”, Math. USSR-Izv., 28:3 (1987), 445–465  mathnet  crossref  mathscinet  zmath
    4. O. I. Bogoyavlenskii, “Some constructions of integrable dynamical systems”, Math. USSR-Izv., 31:1 (1988), 47–75  mathnet  crossref  mathscinet  zmath
    5. R. G. Novikov, G. M. Henkin, “The $\bar\partial$-equation in the multidimensional inverse scattering problem”, Russian Math. Surveys, 42:3 (1987), 109–180  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Math. USSR-Izv., 35:3 (1990), 629–655  mathnet  crossref  mathscinet  zmath
    7. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. O. I. Bogoyavlenskii, “Breaking solitons. III”, Math. USSR-Izv., 36:1 (1991), 129–137  mathnet  crossref  mathscinet  zmath  adsnasa
    9. O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. V. M. Manuilov, “On the Eigenvalues of the Perturbed Schrödinger Operator with Irrational Magnetic Flow”, Funct. Anal. Appl., 28:2 (1994), 120–122  mathnet  crossref  mathscinet  zmath  isi
    11. V. A. Geiler, V. V. Demidov, “Spectrum of three-dimensional landau operator perturbed by a periodic point potential”, Theoret. and Math. Phys., 103:2 (1995), 561–569  mathnet  crossref  mathscinet  zmath  isi
    12. V. A. Geiler, V. A. Margulis, I. I. Chuchaev, “On lacunae in the spectrum of the three-dimensional periodic Schrödinger operator with a magnetic field”, Russian Math. Surveys, 50:1 (1995), 198–199  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. O. K. Sheinman, “Weil Modules with Highest Weight for Affine Lie Algebras on Riemann Surfaces”, Funct. Anal. Appl., 29:1 (1995), 44–55  mathnet  crossref  mathscinet  zmath  isi
    14. V. A. Geiler, V. A. Margulis, “Point perturbation-invariant solutions of the Schrödinger equation with a magnetic field”, Math. Notes, 60:5 (1996), 575–580  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. S. P. Novikov, I. A. Dynnikov, “Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds”, Russian Math. Surveys, 52:5 (1997), 1057–1116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    17. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. K. V. Pankrashin, “Locality of Quadratic Forms for Point Perturbations of Schrödinger Operators”, Math. Notes, 70:3 (2001), 384–391  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. J. Brüning, S. Yu. Dobrokhotov, K. V. Pankrashin, “The Asymptotic Form of the Lower Landau Bands in a Strong Magnetic Field”, Theoret. and Math. Phys., 131:2 (2002), 704–728  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. V. A. Vassiliev, “Spaces of Hermitian operators with simple spectra and their finite-order cohomology”, Mosc. Math. J., 3:3 (2003), 1145–1165  mathnet  crossref  mathscinet  zmath
    21. I. A. Taimanov, “On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves”, Siberian Math. J., 44:4 (2003), 686–694  mathnet  crossref  mathscinet  zmath  isi  elib
    22. P. G. Grinevich, A. E. Mironov, S. P. Novikov, “Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for spin-$1/2$ particles”, Theoret. and Math. Phys., 164:3 (2010), 1110–1127  mathnet  crossref  crossref  adsnasa  isi
    23. P. G. Grinevich, A. E. Mironov, S. P. Novikov, “On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator”, Russian Math. Surveys, 70:2 (2015), 299–329  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    24. L. I. Danilov, “O spektre dvumernogo operatora Shredingera s odnorodnym magnitnym polem i periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 51 (2018), 3–41  mathnet  crossref  elib
    25. Yu. A. Kordyukov, I. A. Taimanov, “Trace formula for the magnetic Laplacian”, Russian Math. Surveys, 74:2 (2019), 325–361  mathnet  crossref  crossref  adsnasa  isi  elib
    26. L. I. Danilov, “Spectrum of the Landau Hamiltonian with a periodic electric potential”, Theoret. and Math. Phys., 202:1 (2020), 41–57  mathnet  crossref  crossref  isi  elib
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