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Uspekhi Mat. Nauk, 1987, Volume 42, Issue 6(258), Pages 77–98 (Mi umn2692)  

This article is cited in 22 scientific papers (total in 23 papers)

Semiclassical approximation for equations with periodic coefficients

V. S. Buslaev

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English version:
Russian Mathematical Surveys, 1987, 42:6, 97–125

Bibliographic databases:

UDC: 517.9
MSC: 81Q20, 81Q05, 81S30, 37Jxx, 35Q40
Received: 20.12.1986
Revised: 20.03.1987

Citation: V. S. Buslaev, “Semiclassical approximation for equations with periodic coefficients”, Uspekhi Mat. Nauk, 42:6(258) (1987), 77–98; Russian Math. Surveys, 42:6 (1987), 97–125

Citation in format AMSBIB
\by V.~S.~Buslaev
\paper Semiclassical approximation for equations with periodic coefficients
\jour Uspekhi Mat. Nauk
\yr 1987
\vol 42
\issue 6(258)
\pages 77--98
\jour Russian Math. Surveys
\yr 1987
\vol 42
\issue 6
\pages 97--125

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    This publication is cited in the following articles:
    1. M. V. Karasev, “New global asymptotics and anomalies for the problem of quantization of the adiabatic invariant”, Funct. Anal. Appl., 24:2 (1990), 104–114  mathnet  crossref  mathscinet  zmath  isi
    2. G. Nenciu, “Dynamics of band electrons in electric and magnetic fields: rigorous justification of the effective Hamiltonians”, Rev Mod Phys, 63:1 (1991), 91  crossref  mathscinet  adsnasa  isi
    3. C. Gerard, A. Martinez, J. Sjöstrand, “A mathematical approach to the effective Hamiltonian in perturbed periodic problems”, Comm Math Phys, 142:2 (1991), 217  crossref  mathscinet  zmath  adsnasa  isi
    4. Werner Horn, “Semindeshclassical constructions in solid state physics”, Communications in Partial Differential Equations, 16:2-3 (1991), 255  crossref
    5. V Grecchi, M Maioli, A Sacchetti, J Phys A Math Gen, 26:7 (1993), L379  crossref  mathscinet  zmath  adsnasa  isi
    6. V Grecchi, A Sacchetti, J Phys A Math Gen, 27:4 (1994), 1393  crossref  mathscinet  zmath  adsnasa  isi
    7. Herbert Spohn, “Long Time Asymptotics for Quantum Particles in a Periodic Potential”, Phys. Rev. Lett, 77:7 (1996), 1198  crossref
    8. O. M. Kiselev, “Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients”, Sb. Math., 190:2 (1999), 233–254  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. M Dimassi, J C Guillot, J Ralston, “Semiclassical asymptotics in magnetic Bloch bands”, J Phys A Math Gen, 35:35 (2002), 7597  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. V. V. Belov, S. Yu. Dobrokhotov, S. O. Sinitsyn, “Asymptotic solutions of the Schrödinger equation in thin tubes”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S13–S23  mathnet  mathscinet  zmath  elib
    11. Mouez Dimassi, Maher Zerzeri, “A local trace formula for resonances of perturbed periodic Schrödinger operators”, Journal of Functional Analysis, 198:1 (2003), 142  crossref
    12. V. V. Belov, S. Yu. Dobrokhotov, T. Ya. Tudorovskii, “Asymptotic Solutions of Nonrelativistic Equations of Quantum Mechanics in Curved Nanotubes: I. Reduction to Spatially One-Dimensional Equations”, Theoret. and Math. Phys., 141:2 (2004), 1562–1592  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. V. S. Buslaev, M. V. Buslaeva, A. Grigis, “Adiabatic asymptotics of the reflection coefficient”, St. Petersburg Math. J., 16:3 (2005), 437–452  mathnet  crossref  mathscinet  zmath
    14. Mouez Dimassi, “Spectral shift function and resonances for slowly varying perturbations of periodic Schrödinger operators”, Journal of Functional Analysis, 225:1 (2005), 193  crossref
    15. M. Dimassi, J.-C. Guillot, J. Ralston, “Gaussian Beam Construction for Adiabatic Perturbations”, Math Phys Anal Geom, 9:3 (2007), 187  crossref  mathscinet  isi
    16. D. I. Borisov, R. R. Gadyl'shin, “The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis”, Sb. Math., 198:8 (2007), 1063–1093  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. A. A. Fedotov, “Complex WKB method for adiabatic perturbations of a periodic Schrödinger operator”, J. Math. Sci. (N. Y.), 173:3 (2011), 320–339  mathnet  crossref
    18. Mouez Dimassi, “Resonances for Perturbed Periodic Schrödinger Operator”, Advances in Mathematical Physics, 2012 (2012), 1  crossref
    19. V. M. Babich, A. M. Budylin, L. A. Dmitrieva, A. I. Komech, S. B. Levin, M. V. Perel', E. A. Rybakina, V. V. Sukhanov, A. A. Fedotov, “On the mathematical work of Vladimir Savel'evich Buslaev”, St. Petersburg Math. J., 25:2 (2014), 151–174  mathnet  crossref  mathscinet  zmath  isi  elib
    20. A. A. Fedotov, “Monodromization method in the theory of almost-periodic equations”, St. Petersburg Math. J., 25:2 (2014), 303–325  mathnet  crossref  mathscinet  zmath  isi  elib
    21. V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source”, Proc. Steklov Inst. Math., 281 (2013), 161–178  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    22. V. V. Grushin, S. Yu. Dobrokhotov, “Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations”, Math. Notes, 95:3 (2014), 324–337  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    23. St. Petersburg Math. J., 29:2 (2018), 399–422  mathnet  crossref  mathscinet  isi  elib
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