On exponential decay of solutions of Schrödinger and Dirac equations : bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum
Nenciu, Gheorghe
Journées équations aux dérivées partielles, (1994), p. 1-10 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1994-01-01
@article{JEDP_1994____A7_0,
     author = {Nenciu, Gheorghe},
     title = {On exponential decay of solutions of Schr\"odinger and Dirac equations : bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1994},
     pages = {1-10},
     zbl = {0948.35506},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_1994____A7_0}
}

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), pp. 1-10. http://gdmltest.u-ga.fr/item/JEDP_1994____A7_0/

[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. | Zbl 0503.35001

[BG] A. Berthier-(Boutet De Monvel) and V. Georgescu, On the point spectrum of Dirac operators, J. Funct. Analysis 71, 309-338 (1987). | MR 89b:35131 | Zbl 0655.47043

[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.

[BCD] Ch. Briet, J.-M. Combes and P. Duclos, Spectral stability under tunneling, Comm. Math. Phys. 126, 133 (1989) | MR 91e:35154 | Zbl 0702.35189

[C] U. Carlson, An infinite number of wells in the semiclasical limit, Asymp. Analysis 3, 189-214 (1989). | Zbl 0727.35094

[CT] J.-M. Combes and L. Thomas, Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators, Commun. Math. Phys. 34, 251-270 (1973). | MR 52 #12611 | Zbl 0271.35062

[CFKS] H. Cycon, R. Froese, W. Kirsch and B. Simon, Schrödinger operators, Berlin, Springer 1987. | Zbl 0619.47005

[D] F. Daumer, Equation de Schrödinger dans l'aproximation du tightbinding, Thse, Universit de Nantes, 1990.

[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). | MR 84c:35034 | Zbl 0514.35024

[GT] D. Gilbarg and N. Trudinger, Elliptic Partial Differential equations of Second Order, 2nd edition, New York, Springer 1983. | MR 86c:35035 | Zbl 0562.35001

[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). | MR 95e:35049 | Zbl 0814.35080

[HS1] B. Helffer and J. Sjostrand, Multiple wells in the semiclassical limit, Commun. PDE 9, 337-408 (1984). | MR 86c:35113 | Zbl 0546.35053

[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). | MR 87i:35161 | Zbl 0597.35023

[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). | Numdam | MR 91c:35043 | Zbl 0699.35205

[H1] I. Herbst, Lower bounds in cones for solutions to the Schrödinger equation, J. d'Analyse Math. 47, 151-174 (1986). | MR 88c:35044 | Zbl 0627.35022

[H2] I. Herbst, Perturbation theory for the decay rate of eigenfunctions in the generalised N-body problem, Commun. Math. Phys. 158, 517-536 (1993). | MR 95e:81244 | Zbl 0819.35105

[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). | Numdam | Zbl 0755.35106

[RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics IV : Analysis of Operators, New York, Academic 1978. | MR 58 #12429c | Zbl 0401.47001

[W] X. P. Wang, Puits multiples pour l'operator de Dirac, Ann. Inst. Henri Poincar 43, 269-319 (1985). | Numdam | Zbl 0614.35074