Une formule de traces pour l’opérateur de Schrödinger dans ℝ 3

Yves Colin de Verdière

Annales scientifiques de l'École Normale Supérieure (1981)

  • Volume: 14, Issue: 1, page 27-39
  • ISSN: 0012-9593

How to cite

top

Colin de Verdière, Yves. "Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb {R}^3$." Annales scientifiques de l'École Normale Supérieure 14.1 (1981): 27-39. <http://eudml.org/doc/82065>.

@article{ColindeVerdière1981,
author = {Colin de Verdière, Yves},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {trace formula; Schrödinger operator; Fredholm determinant},
language = {fre},
number = {1},
pages = {27-39},
publisher = {Elsevier},
title = {Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb \{R\}^3$},
url = {http://eudml.org/doc/82065},
volume = {14},
year = {1981},
}

TY - JOUR
AU - Colin de Verdière, Yves
TI - Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb {R}^3$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1981
PB - Elsevier
VL - 14
IS - 1
SP - 27
EP - 39
LA - fre
KW - trace formula; Schrödinger operator; Fredholm determinant
UR - http://eudml.org/doc/82065
ER -

References

top
  1. [A-S] P. ALSHOLM et G. SCHMIDT, Spectral and Scattering Theory for Schrödinger Operators (Arch. Rat. Mech. Anal., vol. 40, 1971, p. 281-311). Zbl0226.35076MR43 #5352
  2. [B] V. S. BUSLAEV, Scattered Plane waves, Spectral Asymptotics and Trace Formulas in Exterior Problems (Dokl. Akad. Nauk S.S.S.R., vol. 197, 1971, p. 591-595). Zbl0224.47023MR43 #3840
  3. [B-G-M] M. BERGER, P. GAUDUCHON et E. MAZET, Le spectre d'une variété riemannienne (Lecture Notes in Math., vol. 194, 1971). Zbl0223.53034MR43 #8025
  4. [B-K] M. S. BIRMAN et M. G. KREIN, On the Theory of wave Operators and Scattering Operators (Dokl. Akad. Nauk S.S.S.R., vol. 144, 1962, p. 475-478). Zbl0196.45004MR25 #2447
  5. [CV] Y. COLIN DE VERDIÈRE, Spectre du laplacien et longueurs des géodésiques périodiques II (Compositio Mathematica, vol. 27, 1973, p. 159-184). Zbl0281.53036MR50 #1293
  6. [F-Z] P. FADDEEV et V. ZAKHAROV, KdV Equation : a Completely Integrable Hamiltonian System (Funct. Anal. and Appl. vol. 5, 1971, p. 280-288). Zbl0257.35074
  7. [G-M-G-T] V. GLASER, A. MARTIN, H. GROSSE et W. THIRRING, A Family of Optimal Conditions for the Absence of Bound States in a Potential. Studies in Math. Phys., LIEB, SIMON et WIGHTMANN, éd., Princeton, 1976, p. 169-194. Zbl0332.31004
  8. [J-K] A. JENSEN et T. KATO, Asymptotic behaviour of the Scattering Phase for Exterior Domains (Comm. P.D.E., vol. 3, 1978, p. 1165-1195). Zbl0419.35067MR80g:35098
  9. [K-M] H. P. MCKEAN et VAN MOERBECKE, The Spectrum of Hill's Equation (Invent. Math., vol. 30, 1975, p. 217-254). Zbl0319.34024MR53 #936
  10. [L-P1] P. LAX et R. S. PHILLIPS, Scattering Theory for Automorphic Functions (Annals Math. Studies, 1976, Princeton). Zbl0362.10022MR58 #27768
  11. [L-P 2] P. LAX et R. S. PHILLIPS, The Time Delay Operator and a Related Trace Formula. Topics in Functional Analysis, GOHBERG et M. KAC, ed., Academic Press, 1978, p. 197-215. Zbl0463.47006MR80j:47010
  12. [L-T] E. LIEB et W. THIRRING, Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian... Studies in Math. Phys., LIEB, SIMON et WIGHTMANN, éd., Princeton, 1976, p. 269-304. Zbl0342.35044
  13. [MR] A. MAJDA et J. RALSTON, An Analogue of Weyl's Theorem for Unbounded Domains I, II et III (Duke Math. J., vol. 45, p. 183-196 et 513-536 ; vol. 46, 1979, p. 725-731). Zbl0408.35069
  14. [N] R. NEWTON, Non Central Potentiels : the Generalized Levinson Theorem and the Structure of the Spectrum (J. Math. Phys., vol. 18, 1977, p. 1348-1357). MR56 #4509
  15. [R-S] M. REED et B. SIMON, Scattering Theory, Academic Press, 1979. Zbl0405.47007
  16. [S 1] B. SIMON, Quantum Mechanics for Hamiltonians defined as Quadratic Forms, Princeton, 1971. Zbl0232.47053
  17. [S 2] B. SIMON, Trace Ideals and their Applications, Cambridge, 1979. Zbl0423.47001MR80k:47048
  18. [S 3] B. SIMON, On the Number of Bound States of the Two-Body Schrödinger Operators. A review. Studies in Math. Phys., LIEB, SIMON et WIGHTMANN, éd., Princeton, 1976, p. 305-326. Zbl0349.35022
  19. [Z-K] C. ZEMACH et A. KLEIN, The Born Expansion in non Relativistic Quantum Theory, I (Nuovo Cimento, vol. 10, 1958, p. 1078-1087). Zbl0084.44803MR21 #580

Citations in EuDML Documents

top
  1. Hart F. Smith, Maciej Zworski, [unknown]
  2. Jean-Marc Bouclet, Asymptotic behavior of regularized scattering phases for long range perturbations
  3. A. V. Sobolev, Efficient bounds for the spectral shift function
  4. Y. Colin de Verdière, La matrice de Scattering pour l'opérateur de Schrödinger sur la droite réelle
  5. D. Robert, Approximation semi-classique de la phase de diffusion pour un potentiel (d'après un travail de D. Robert et H. Tamura)
  6. D. Robert, Asymptotique de la phase de diffusion à haute énergie pour des perturbations du laplacien
  7. Gilles Carron, Déterminant relatif et la fonction Xi
  8. Werner Müller, Relative determinants of elliptic operators and scattering theory
  9. Veselin Petkov, Georgi Popov, Asymptotic behaviour of the scattering phase for non-trapping obstacles
  10. D. Robert, Asymptotique de la phase de diffusion à haute énergie pour des perturbations du second ordre du laplacien

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.