Asymptotic completeness in long range scattering. II

Pl. Muthuramalingam; Kalyan B. Sinha

Annales scientifiques de l'École Normale Supérieure (1985)

  • Volume: 18, Issue: 1, page 57-87
  • ISSN: 0012-9593

How to cite

top

Muthuramalingam, Pl., and Sinha, Kalyan B.. "Asymptotic completeness in long range scattering. II." Annales scientifiques de l'École Normale Supérieure 18.1 (1985): 57-87. <http://eudml.org/doc/82156>.

@article{Muthuramalingam1985,
author = {Muthuramalingam, Pl., Sinha, Kalyan B.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {long range scattering; Asymptotic completeness; short range potential; long range potential},
language = {eng},
number = {1},
pages = {57-87},
publisher = {Elsevier},
title = {Asymptotic completeness in long range scattering. II},
url = {http://eudml.org/doc/82156},
volume = {18},
year = {1985},
}

TY - JOUR
AU - Muthuramalingam, Pl.
AU - Sinha, Kalyan B.
TI - Asymptotic completeness in long range scattering. II
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1985
PB - Elsevier
VL - 18
IS - 1
SP - 57
EP - 87
LA - eng
KW - long range scattering; Asymptotic completeness; short range potential; long range potential
UR - http://eudml.org/doc/82156
ER -

References

top
  1. [1] W. O. AMREIN, J. M. JAUCH and K. B. SINHA, Scattering Theory in Quantum Mechanics, W. Benjamin, Reading, 1977. Zbl0376.47001MR58 #14631
  2. [2] P. ALSHOLM, Wave Operators for Long Range Scattering (J. Math. Anal. Appl., Vol. 59, 1977, p. 550). Zbl0359.47006MR58 #1740
  3. [3] L. HÖRMANDER, The Existence of Wave Operators in Scattering Theory, (Math. Zeit., Vol. 146, 1976, pp. 69-91). Zbl0319.35059MR52 #14691
  4. [4] A. M. BERTHIER and P. COLLET, Wave Operators for Momentum Dependent long Range Potential (Ann. Inst. Henri-Poincaré, Section A, Vol. 27, 1977, pp. 279-293). Zbl0346.47010MR57 #2303
  5. [5] W. O. AMREIN, Ph. A. MARTIN and B. MISRA, On the Asymptotic Condition of Scattering Theory (Helv. Phys. Acta, Vol. 43, 1970, pp. 313-344). Zbl0195.56101MR46 #8586
  6. [6] J. D. DOLLARD, Asymptotic Convergence and the Coulomb Interaction (J. Math. Phys., Vol. 5, 1964, pp. 729-738). MR29 #921
  7. [7] R. LAVINE, Absolute Continuity of Positive Spectrum for Schrödinger Operators with Long Range Potentials (J. Func. Anal., Vol. 12, 1973, pp. 30-54). Zbl0246.47017MR49 #7624
  8. [8] T. IKEBE, Spectral Representations for Schrödinger Operators with Long Range Potentials. Perturbation by short range potentials (Publ. Res. Inst. Math. Sc., Vol. 11, 1976, pp. 551-558). Zbl0345.35032MR55 #13092
  9. [9] Y. SAITO, Spectral Representations for Schrödinger Operators with long Range potential (Lecture Notes in Math. No. 727, Berlin. Heildelberg, New York, Springer-Verlag, 1979). Zbl0414.47012MR81a:35083
  10. [10] J. WEIDMANN, Über Spectraltheorie von SturmLiouville-Operatoren (Math. Zeit., Vol. 98, 1967, pp. 268-302). Zbl0168.12301MR35 #4769
  11. [11] V. GEORGESCU, Méthodes stationnaires pour des potentiels à longue portée à symétrie sphérique (Thèse, Université de Genève, 1974). 
  12. [12] T. IKEBE and H. ISOZAKI, A Stationary Approach to the Existence and Completeness of Long Range wave Operators, preprint, Kyoto Univ., 1980. Zbl0496.35069
  13. [13] H. KITADA, Scattering Theory for Schrodinger Operators with Long Range Potentials II (J. Math. Soc. Japan, Vol. 30, 1978, pp. 603-632). Zbl0388.35055MR58 #30372b
  14. [14] S. AGMON, Some new Results in Spectral and Scattering Theory of Differential Operators on L²(Rn) [Séminaire Goulaouic-Schwartz, 1978-1979, Centre de Mathématiques, Palaiseau (Lecture notes)]. Zbl0406.35052
  15. [15] L. E. THOMAS, On the Algebraic Theory of Scattering (J. Func. Anal., Vol. 15, 1974, pp. 364-377). Zbl0283.47006MR54 #6783
  16. [16] V. ENSS, Asymptotic Completeness for Quantum Mechanical Potential Scattering II. Singular and Long Range Potentials (Ann. Phys. New York, Vol. 119, 1979, pp. 117-132). Zbl0408.47009MR80k:81144
  17. [17] V. ENSS, Geometric Methods in Spectral and Scattering Theory of Schrödinger Operators, Section 7 in (Rigorous Atomic and Molecular Physics), G. VELO and A. WEIGHTMAN eds., New York, Plenum, 1981. 
  18. [18] P. A. PERRY, Propagation of States in Dilation Analytic Potentials and Asymptotic Completeness (Comm. Math. Phys., Vol. 81, 1981, pp. 243-259). Zbl0471.47007MR84f:81097
  19. [19] Pl. MUTHURAMALINGAM and K. B. SINHA, Asymptotic Evoluation of Certain Observables and Completeness in Coulomb Scattering I (J. Func. Analysis, Vol. 55, 1983). Zbl0531.47008
  20. [20] T. KATO, Perturbation Theory for Linear Operators, Springer, Berlin, 1966. Zbl0148.12601MR34 #3324
  21. [21] M. REED and B. SIMON, Methods of Modern Mathematical Physics, II. Fourier Analysis, Self Adjointness, Academic Press, New York, 1972. Zbl0308.47002
  22. [22] M. REED and B. SIMON, Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, New York, 1979. Zbl0405.47007MR80m:81085
  23. [23] M. REED and B. SIMON, Methods of Modern Mathematical Physics, IV. Analysis of Operators, Academic Press, New York, 1978. Zbl0401.47001MR58 #12429c
  24. [24] P. A. PERRY, Mellin Transforms and Scattering Theory, I. Short Range Potentials (Duke Math. J., Vol. 47, 1980, pp. 187-193). Zbl0445.47009MR81c:35101
  25. [25] E. B. DAVIES, Quantum Theory of Open Systems, Academic Press, New York, 1976. Zbl0388.46044MR58 #8853
  26. [26] E. B. DAVIES, On Enss' Approach to Scattering Theory (Duke Math. J. Vol. 47, 1980, pp. 171-185). Zbl0434.47014MR81c:81046
  27. [27] J. GINIBRE, La Méthode "dépendant du temps" dans le problème de la complétude asymptotique, preprint, Université de Paris-Sud, LP THE 80/10, 1980. 
  28. [28] E. MOURRE, Opérateurs conjugués et propriétés de propagation (Commun. Math. Phys., Vol. 91, 1983, pp. 279-300). Zbl0543.47041MR86h:47031
  29. [29] A. JENSEN, E. MOURRE and P. PERRY, Multiple Commutator Estimates and Resolvent Smoothness in Quantum Scattering Theory, Preprint, 1983, Caltech, CA 91125. Zbl0561.47007

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.