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ЖУРНАЛЫ // Алгебра и анализ

Алгебра и анализ, 2018, том 30, выпуск 3, страницы 76–92 (Mi aa1596)

Asymptotics of the ground state energy in the relativistic settings
V. Ivrii

Список литературы

1. Bach V., “Error bound for the Hartree–Fock energy of atoms and molecules”, Comm. Math. Phys., 147:3 (1992), 527–548  crossref  mathscinet  zmath  adsnasa
2. Daubechies I., “An uncertainty principle for fermions with generalized kinetic energy”, Comm. Math. Phys., 90:4 (1983), 511–520  crossref  mathscinet  zmath  adsnasa
3. Erdös L., Fournais S., Solovej J. P., “Scott correction for large atoms and molecules in a self-generated magnetic field”, Comm. Math. Phys., 312:3 (2012), 847–882  crossref  mathscinet  zmath  adsnasa
4. Erdös L., Fournais S., Solovej J. P., “Relativistic Scott correction in self-generated magnetic fields”, J. Math. Phys., 53 (2012), 095202  crossref  mathscinet  zmath  adsnasa  elib
5. Frank R. L., Lieb E. H., Seiringer R., “Hardy–Lieb–Thirring inequalities for fractional Schrödinger operators”, J. Amer. Math. Soc., 21:4 (2008), 925–950  crossref  mathscinet  zmath
6. Frank R. L., Siedentop H., Warzel S., “The ground state energy of heavy atoms: relativistic lowering of the leading energy correction”, Comm. Math. Phys., 278:2 (2008), 549–566  crossref  mathscinet  zmath  adsnasa  elib
7. Graf G. M., Solovej J. P., “A correlation estimate with applications to quantum systems with Coulomb interactions”, Rev. Math. Phys., 6:5a (1994), 977–997  crossref  mathscinet  zmath; Adv. Ser. Math. Phys., 20, World Sci., Singapure, 1994, 142–166  crossref
8. Herbst I. W., “Spectral theory of the operator $(p^2+m^2)^{1/2}-Ze^2/r$”, Comm. Math. Phys., 53:3 (1977), 285–294  crossref  mathscinet  zmath  adsnasa
9. Ivrii V., Microlocal analysis, sharp spectral asymptotics and applications, http://www.math.toronto.edu/ivrii/monsterbook.pdf
10. Ivrii V., Asymptotics of the ground state energy in the relativistic settings and with self-generated magnetic field, arXiv: 1708.07737
11. Lieb E. H., Thirring W. E., “Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities”, Essays Honor Valentine Bargmann, Stud. Math. Phys., Princeton Univ. Press, Princeton, NJ, 1976, 269–303
12. Lieb E. H., Yau H. T., “The stability and instability of relativistic matter”, Comm. Math. Phys., 118:2 (1988), 177–213  crossref  mathscinet  zmath  adsnasa
13. Solovej J. P., Sørensen T. Ø., Spitzer W. L., “The relativistic Scott correction for atoms and molecules”, Comm. Pure Appl. Math., 63:1 (2010), 9–118  crossref  mathscinet


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