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TMF, 1987, Volume 73, Number 3, Pages 430–442 (Mi tmf5645)  

This article is cited in 7 scientific papers (total in 8 papers)

Adiabatic perturbation of periodic potential. II

V. S. Buslaev, L. A. Dmitrieva


Abstract: For the equation $-\psi" +p(x)\psi +q(\varepsilon x)\psi=0$, $p$ – periodic function, $\varepsilon\to 0$), behaviour of solutions in neighbourhood of two close turning points is studied. The results give mathematically consistent description of the electric breakdown effect in the Block electron theory.

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English version:
Theoretical and Mathematical Physics, 1987, 73:3, 1320–1329

Bibliographic databases:

Received: 06.05.1986

Citation: V. S. Buslaev, L. A. Dmitrieva, “Adiabatic perturbation of periodic potential. II”, TMF, 73:3 (1987), 430–442; Theoret. and Math. Phys., 73:3 (1987), 1320–1329

Citation in format AMSBIB
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\by V.~S.~Buslaev, L.~A.~Dmitrieva
\paper Adiabatic perturbation of periodic potential.~II
\jour TMF
\yr 1987
\vol 73
\issue 3
\pages 430--442
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=939788}
\zmath{https://zbmath.org/?q=an:0643.34068}
\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 73
\issue 3
\pages 1320--1329
\crossref{https://doi.org/10.1007/BF01041915}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987P129500009}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. A. A. Pozharskii, “A crystal with a singular potential in a homogeneous electric field”, Theoret. and Math. Phys., 123:1 (2000), 524–538  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. A. Pozharskii, “On the nature of the Stark–Wannier spectrum”, St. Petersburg Math. J., 16:3 (2005), 561–581  mathnet  crossref  mathscinet  zmath
    3. A. A. Pozharskii, “Semicrystal with a singular potential in an accelerating electric field”, Theoret. and Math. Phys., 146:3 (2006), 343–360  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Glebov, S, “Weakly Nonlinear Dispersive Waves under Parametric Resonance Perturbation”, Studies in Applied Mathematics, 124:1 (2010), 19  crossref  isi
    5. 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
    6. 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
    7. 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
    8. A. R. Bikmetov, I. Kh. Khusnullin, “Perturbation of Hill operator by narrow potentials”, Russian Math. (Iz. VUZ), 61:7 (2017), 1–10  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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