On spectral properties of adiabatically perturbed Schroedinger operators with periodic potentials

V. Buslaev

Séminaire Équations aux dérivées partielles (Polytechnique) (1990-1991)

  • page 1-15

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Buslaev, V.. "On spectral properties of adiabatically perturbed Schroedinger operators with periodic potentials." Séminaire Équations aux dérivées partielles (Polytechnique) (1990-1991): 1-15. <http://eudml.org/doc/112016>.

@article{Buslaev1990-1991,
author = {Buslaev, V.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {spectrum; resonances},
language = {eng},
pages = {1-15},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {On spectral properties of adiabatically perturbed Schroedinger operators with periodic potentials},
url = {http://eudml.org/doc/112016},
year = {1990-1991},
}

TY - JOUR
AU - Buslaev, V.
TI - On spectral properties of adiabatically perturbed Schroedinger operators with periodic potentials
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1990-1991
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 15
LA - eng
KW - spectrum; resonances
UR - http://eudml.org/doc/112016
ER -

References

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  1. [1] Buslaev, V.S., On adiabatic perturbation of a periodic potential, Teoreticheskaya i matematichskaya fizika58, N 2, (1984), 233-243. Zbl0534.34064MR743409
  2. [2] Buslaev, V.S., Semiclassical approximation for equations with periodic coefficients, Russian Mathem. Surveys42: (1987), 97-125. Zbl0698.35130MR933996
  3. [3] Guillot, J.C.; Ralston, J. and Trubowitz, E., Semi-classical asymptotics in solid state physics, Commun. Math. Phys.116, (1988), 401-415. Zbl0672.35014MR937768
  4. [4] Maslov V.P., Nonstandard characteristics in asymptotic problems, Russian Mathem. Surveys38: 6, (1983), 3-36. Zbl0562.35007MR728722
  5. [5] Buslaev, V.S., Dmitrieva, L.A., Spectral properties of the Bloch electrons in external fields, Preprint University of Berkeley PAM-477, (1989). Zbl0725.34097
  6. [6] Buslaev, V.S., Dmitrieva, L.A., Bloch electrons in the external electric field, in Schroedinger operators, standard and non-standard (eds P. Exner and P. Seba), World Scientific, Singapore, (1989), 103-129. Zbl0725.34097MR1091994
  7. [7] Buslaev, V.S., Dmitrieva, L.A., A Bloch electron in an external field, Leningrad Math. J.1: 2, (1990), 287-320. Zbl0726.34070MR1025153
  8. [8] Buslaev, V.S., Spectral properties of the operators Hψ= -ψxx + p(x)ψ + V(εx), p is periodic, Operator Theory: Advances and Applications46, (1990), 85-107. Zbl0723.47042
  9. [9] Buslaev, V.S., Spectral properties of adiabatically perturbed differential operators with periodic coefficients, in Recent Development in Quantum Mechanics, Mathematical Physics Studies 12 (eds A. Boutet de Monvel, P. Dita, G. Nenciu, R. Purice), Kluwer Academic Publishers, (1991), 97-112. Zbl0726.34068MR1189400
  10. [10] Buslaeva, M.V., Asymptotical dynamics and spectral analysis of the one-dimensional Schroedinger operators with accelerating potentials, in Problems in Mathematical Physics 11, (ed M. Birman), Leningrad University, (1986), 67-77. Zbl0599.47013MR857108
  11. [11] Buslaeva, M.V., Asymptotical dynamics and spectral analysis of the Schroedinger operator with weakly accelerating potentials, Zapiski Nauchnih SeminarovLOMI164 (ed L. Faddeev), Leningrad, Nauka, (1987), 10-19. Zbl0688.35069MR947325
  12. [12] Buslaev, V.S., Dmitrieva, L.A., Adiabatic perturbation of a periodic potential. II, Teoreticheskaya i matematicheskaya fizika73, (1987), 430-442. Zbl0643.34068MR939788
  13. [13] Bentosela, F., Stark-Wannier resonant states, preprint, Centre de Physique Theorique Marseille, CPT-90/ P.2256, (1990), 11pp Zbl0726.34075MR1189399
  14. [14] Combes, J.M., Hislop P.D., Quantum tunnelling, non trapping and the existence of Stark ladder resonances, J. Phys. A: Math. Gen.23, (1990), 1-11. Zbl0708.35061MR1048780

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