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Semiclassical Spectral Asymptotics and Multiparticle Quantum Theory

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Partial Differential Operators and Mathematical Physics

Part of the book series: Operator Theory Advances and Applications ((OT,volume 78))

Abstract

In this talk I would like to present the very first results of my intervention to the Multiparticle Quantum Theory (MQT). A lot of nice results were obtained by mathematical physicists but the Theory of Semiclassical Spectral Asymptotics (TSSA) was applied only in a few papers and I believe that the systematic application will provide some progress. This is my long term project. However, it is vital to combine methods of TSSA and MQT. The first talk with this subject was given in École Polytechnique 2 1/2 months ago but I managed to advance after and this address is improved, corrected and advanced version of that talk.

Work was partially supported by NSERC grant OGP0138277.

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References

  1. V. Bach. Error bound for the Hartree-Fork energy of atoms and molecules, Commun. Math. Phys., 147 (1992), 527 – 548.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. Fefferman, L. Seco. The ground state energy of a large atom, Bull. A.M.S 23 (1990), 525 - 530.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Feferman, L. Seco. On the Dirac and Schwinger corrections to the ground state energy of an atom, Adv. Math. (to appear).

    Google Scholar 

  4. G.M. Graf, P. Solovej. A correlation estimate with applications to quantum systems with Coulomb interactions (to appear).

    Google Scholar 

  5. V. Ivrii. Semiclassical microlocal analysis and precise spectral asymptotics. Chapters 4, 10, 12 (Preprints 1, 7, 8), Ecole Polytechnique, (1990-92). Revised version is available by e-mail.

    Google Scholar 

  6. V. Ivrii. Semi-classical asymptotics for exchange energy. Sem. EDP, Ecole Polytechnique, 1993/94.

    Google Scholar 

  7. V. Ivrii. Around Scott correction term(s). Travaux Conf. EDP Sant Jean de Monts (1994) (to appear).

    Google Scholar 

  8. V. Ivrii, I.M. Sigal. As ymptotics of the ground state energies of large Coulomb systems. Ann. Math 138 (1993), 243 – 335.

    Article  MathSciNet  MATH  Google Scholar 

  9. E.H. Lieb. The stability of matter: from atoms to stars (Selecta). Springer¬Verlag (1991).

    Google Scholar 

  10. I.M. Sigal. Lectures on large Coulomb systems (to appear).

    Google Scholar 

  11. A. Sobolev. The quasi-classical asymptotics of local Riesz means for the Schrodinger operator in a strong homogeneous magnetic field, Duke Math. J., (1994).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, 100, St. George Str., Toronto, Ontario, M5S 1A1, Canada

    Victor Ivrii

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  1. Victor Ivrii
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Technische Universität Clausthal, Erzstrasse 1, 38678, Clausthal-Zellerfeld, Germany

    Michael Demuth

  2. Institut für Mathematik, Max Planck-Arbeitsgruppe “Partielle Differentialgleichungen and Komplexe Analysis” Universität Potsdam, Postfach 60 15 53, 14415, Potsdam, Germany

    Bert-Wolfgang Schulze

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© 1995 Birkhäuser Verlag Basel/Switzerland

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Ivrii, V. (1995). Semiclassical Spectral Asymptotics and Multiparticle Quantum Theory. In: Demuth, M., Schulze, BW. (eds) Partial Differential Operators and Mathematical Physics. Operator Theory Advances and Applications, vol 78. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9092-2_22

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  • DOI: https://doi.org/10.1007/978-3-0348-9092-2_22

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9903-1

  • Online ISBN: 978-3-0348-9092-2

  • eBook Packages: Springer Book Archive

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