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Recent Developments in Quantum Mechanics pp 97–112Cite as

Spectral Properties of Adiabatically Perturbed Differential Operators with the Periodic Coefficients

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Part of the book series: Mathematical Physics Studies ((MPST,volume 12))

Abstract

We describe the asymptotic structure of the spectrum and the asymptotic behavior of the eigenfunctions of the operators

$$Hz = - {z_{xx}} + p(x)z + v(\varepsilon x)z, $$

p is periodic, 0 ‹ ε “ 1.

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References

  1. Buslaev V.S. (1984) ‘Adiabatic perturbation of a periodic potential’, Teor. Mat. Fiz. 58, 233–243

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  2. Buslaev V.S., Dmitrieva L.A. (1987) ‘Adiabatic perturbation of a periodic potential. II’, Teor. Mat. Fiz. 73, 430–442

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  3. Buslaev V.S. (1987) ‘A semiclassical aproximation to the equation with periodic coefficients’, Sov. Math. Uspekhi, 42, 77–96

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  4. Guillot J.C., Ralston J., Trubovitz E. (1988) ‘Semiclassical asymptotics in solid state physics’, Comm. Math. Phys., 116, 401–415

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  5. Buslaev V.S., Dmitrieva L.A. (1989) ‘Bloch electron in an external field’, Algebra and analysis, 1 N2, 1–29

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  6. Buslaev V.S., Dmitrieva L.A. (1989) ‘Bloch electrons in an external electric field’ in P. Exner, P. Seba (eds.), Schrodinger operators, standard and nonstandard, World Scientific, Singapore, N. J., L., Hong Kong, pp. 101–129

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Author information

Authors and Affiliations

  1. Institute of Physics, Leningrad University, Petrodworetz, Leningrad, 198904, USSR

    V. S. Buslaev

Authors
  1. V. S. Buslaev
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Editor information

Editors and Affiliations

  1. University Paris VII, Paris, France

    Anne Boutet de Monvel

  2. Bucharest University, Bucharest, Romania

    Petre Dita

  3. Theoretical Physics Department, Institute of Atomic Physics, Bucharest, Romania

    Gheorghe Nenciu

  4. Bucharest University, Bucharest, Romania

    Radu Purice

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© 1991 Springer Science+Business Media Dordrecht

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Buslaev, V.S. (1991). Spectral Properties of Adiabatically Perturbed Differential Operators with the Periodic Coefficients. In: Boutet de Monvel, A., Dita, P., Nenciu, G., Purice, R. (eds) Recent Developments in Quantum Mechanics. Mathematical Physics Studies, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3282-4_5

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  • DOI: https://doi.org/10.1007/978-94-011-3282-4_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5449-2

  • Online ISBN: 978-94-011-3282-4

  • eBook Packages: Springer Book Archive

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