On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum

Gheorghe Nenciu

Journées équations aux dérivées partielles (1994)

  • Volume: 1994, page 1-10
  • ISSN: 0752-0360

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Nenciu, Gheorghe. "On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum." Journées équations aux dérivées partielles 1994 (1994): 1-10. <http://eudml.org/doc/93292>.

@article{Nenciu1994,
author = {Nenciu, Gheorghe},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-10},
publisher = {Ecole polytechnique},
title = {On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum},
url = {http://eudml.org/doc/93292},
volume = {1994},
year = {1994},
}

TY - JOUR
AU - Nenciu, Gheorghe
TI - On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum
JO - Journées équations aux dérivées partielles
PY - 1994
PB - Ecole polytechnique
VL - 1994
SP - 1
EP - 10
LA - eng
UR - http://eudml.org/doc/93292
ER -

References

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  1. [A] S. Agmon, Lecture on Exponential decay of Solutions of Second Order Elliptic Equations : Bounds on Eigenfunctions of N- body Schrödinger Operators, Princeton, Princeton University Press, 1982. Zbl0503.35001
  2. [BG] A. Berthier-(Boutet de Monvel) and V. Georgescu, On the point spectrum of Dirac operators, J. Funct. Analysis 71, 309-338 (1987). Zbl0655.47043MR89b:35131
  3. [BNN] A. Boutet de Monvel, A. Nenciu and G. Nenciu, Perturbed periodic hamiltonians : essential spectrum and exponential decay of solutians, submitted to Lett. in Math. Phys. Zbl0848.35103
  4. [BCD] Ch. Briet, J.-M. Combes and P. Duclos, Spectral stability under tunneling, Comm. Math. Phys. 126, 133 (1989) Zbl0702.35189MR91e:35154
  5. [C] U. Carlson, An infinite number of wells in the semiclasical limit, Asymp. Analysis 3, 189-214 (1989). Zbl0727.35094
  6. [CT] J.-M. Combes and L. Thomas, Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators, Commun. Math. Phys. 34, 251-270 (1973). Zbl0271.35062MR52 #12611
  7. [CFKS] H. Cycon, R. Froese, W. Kirsch and B. Simon, Schrödinger operators, Berlin, Springer 1987. Zbl0619.47005
  8. [D] F. Daumer, Equation de Schrödinger dans l'aproximation du tightbinding, Thse, Universit de Nantes, 1990. 
  9. [FH3O2] R. Froese, I. Herbst, M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, L2-exponential lower bounds to solutions of the Schrödinger equation, Commun. Math. Phys. 87, 265-268 (1982). Zbl0514.35024MR84c:35034
  10. [GT] D. Gilbarg and N. Trudinger, Elliptic Partial Differential equations of Second Order, 2nd edition, New York, Springer 1983. Zbl0562.35001MR86c:35035
  11. [HN] B. Helffer and J. Nourrigat, Decroisance a l'infini des functions propres de l'operator de Schrödinger avec champ electromagnetique polynomial, J. d'Analyse Math. 58, 263-275 (1992). Zbl0814.35080MR95e:35049
  12. [HS1] B. Helffer and J. Sjostrand, Multiple wells in the semiclassical limit, Commun. PDE 9, 337-408 (1984). Zbl0546.35053MR86c:35113
  13. [HS2] B. Helffer and J. Sjostrand, Multiple wells in the semi-classical limit III. Interactions through non-resonant wells, Math. Nacht. 124, 263-313 (1985). Zbl0597.35023MR87i:35161
  14. [HS3] B. Helffer and J. Sjostrand, Effect tunnel pour l'equation de Schrödinger avec champ magnetique, Annali Scuola Normale Sup. Pisa 14, 625-657 (1987). Zbl0699.35205MR91c:35043
  15. [H1] I. Herbst, Lower bounds in cones for solutions to the Schrödinger equation, J. d'Analyse Math. 47, 151-174 (1986). Zbl0627.35022MR88c:35044
  16. [H2] I. Herbst, Perturbation theory for the decay rate of eigenfunctions in the generalised N-body problem, Commun. Math. Phys. 158, 517-536 (1993). Zbl0819.35105MR95e:81244
  17. [MP] A. Mohamed and B. Parrise, Approximation des valeurs propres de certaines perturbations singuliers et applications a l'operator de Dirac, Ann. Inst. Henri Poincar 56, 235-277 (1992). Zbl0755.35106
  18. [RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics IV : Analysis of Operators, New York, Academic 1978. Zbl0401.47001MR58 #12429c
  19. [W] X. P. Wang, Puits multiples pour l'operator de Dirac, Ann. Inst. Henri Poincar 43, 269-319 (1985). Zbl0614.35074

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