A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators

Heinz Siedentop; Rudi Weikard

Annales scientifiques de l'École Normale Supérieure (1991)

  • Volume: 24, Issue: 2, page 215-225
  • ISSN: 0012-9593

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Siedentop, Heinz, and Weikard, Rudi. "A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators." Annales scientifiques de l'École Normale Supérieure 24.2 (1991): 215-225. <http://eudml.org/doc/82295>.

@article{Siedentop1991,
author = {Siedentop, Heinz, Weikard, Rudi},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Thomes-Fermi energy; Macke orbitals; phase space localization; Scott type lower bound},
language = {eng},
number = {2},
pages = {215-225},
publisher = {Elsevier},
title = {A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators},
url = {http://eudml.org/doc/82295},
volume = {24},
year = {1991},
}

TY - JOUR
AU - Siedentop, Heinz
AU - Weikard, Rudi
TI - A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1991
PB - Elsevier
VL - 24
IS - 2
SP - 215
EP - 225
LA - eng
KW - Thomes-Fermi energy; Macke orbitals; phase space localization; Scott type lower bound
UR - http://eudml.org/doc/82295
ER -

References

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  1. [1] V. BACH, A Proof of Scott's Conjecture for Ions. [Rep. Math. Phys., (to appear).]. Zbl0732.58042
  2. [2] F. A. BEREZIN, Wick and Anti-Wick Operator Symbols. (Math. U.S.S.R. Sbornik, Vol. 15, 1971, pp. 578-610). Zbl0247.47018MR45 #929
  3. [3] W. HUGHES, An Atomic Energy Lower Bound that Gives Scott's Correction. (Ph. D. thesis, Princeton, Department of Mathematics, 1986). 
  4. [4] W. HUGHES, An Atomic Lower Bound that Agrees with Scott's Correction. (Advances in Mathematics, 1990, pp. 213-270). Zbl0715.46046MR91c:81180
  5. [5] E. H. LIEB, Thomas-Fermi and Related Theories of Atoms and Molecules (Rev. Mod. Phys., 53, 1981, pp. 603-604). Zbl1049.81679MR83a:81080a
  6. [6] E. H. LIEB and B. SIMON, The Thomas-Fermi Theory of Atoms, Molecules and Solids. (Adv. Math., Vol. 23, 1977, pp. 22-116). Zbl0938.81568MR55 #1964
  7. [7] E. H. LIEB and W. E. THIRRING, Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and their Relation to Sobolev Inequalities, in E. H. LIEB, B. SIMON and A. S. WIGHTMAN Ed., Studies in Mathematical Physics : Essays in Honor of Valentine Bargmann, Princeton University Press, Princeton, 1976. Zbl0342.35044
  8. [8] H. SIEDENTOP and R. WEIKARD, On Some Basic Properties of Density Functionals for Angular Momentum Channels. (Rep. Math. Phys., Vol. 28, 1986, pp. 193-218). Zbl0644.46059MR90a:81196
  9. [9] H. SIEDENTOP and R. WEIKARD, On the Leading Correction of the Thomas-Fermi Model : Lower Bound - with an Appendix by A. M. K. Müller. (Invent. Math., 97, 1989, pp. 159-193). Zbl0689.34011MR90k:81285
  10. [10] H. SIEDENTOP and R. WEIKARD, On the Leading Energy Correction for the Statistical Model of the Atom : Interacting Case. (Commun. Math. Phys., Vol. 112, 1987, pp. 471-490). Zbl0920.35120MR89a:81022

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