메뉴 건너뛰기




Volumn 278, Issue 2, 2008, Pages 549-566

The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction

Author keywords

[No Author keywords available]

Indexed keywords


EID: 38749083006     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0397-x     Document Type: Article
Times cited : (32)

References (62)
  • 1
    • 0040810890 scopus 로고
    • Master's thesis, Institut für Mathematische Physik, Technische Universität Braunschweig, Braunschweig, June
    • Bach, V.: Ein Beweis der Scottschen Vermutung für Ionen. Master's thesis, Institut für Mathematische Physik, Technische Universität Braunschweig, Braunschweig, June 1989
    • (1989) Ein Beweis der Scottschen Vermutung für Ionen
    • Bach, V.1
  • 2
    • 38249026162 scopus 로고
    • A proof of Scott's conjecture for ions
    • 2
    • Bach V. (1989). A proof of Scott's conjecture for ions. Rep. Math. Phys. 28(2): 213-248
    • (1989) Rep. Math. Phys. , vol.28 , pp. 213-248
    • Bach, V.1
  • 3
    • 0041723821 scopus 로고
    • Error bound for the Hartree-Fock energy of atoms and molecules
    • Bach V. (1992). Error bound for the Hartree-Fock energy of atoms and molecules. Commun. Math. Phys. 147: 527-548
    • (1992) Commun. Math. Phys. , vol.147 , pp. 527-548
    • Bach, V.1
  • 4
    • 3543044382 scopus 로고    scopus 로고
    • A proof of Scott's correction for matter
    • 1
    • Balodis P. (2004). A proof of Scott's correction for matter. Commun. Math. Phys. 249(1): 79-132
    • (2004) Commun. Math. Phys. , vol.249 , pp. 79-132
    • Balodis, P.1
  • 5
    • 33746896221 scopus 로고    scopus 로고
    • The ground-state energy of heavy atoms according to Brown and Ravenhall: Absence of relativistic effects in leading order
    • 33
    • Cassanas R. and Siedentop H. (2006). The ground-state energy of heavy atoms according to Brown and Ravenhall: absence of relativistic effects in leading order. J. Phys. A 39(33): 10405-10414
    • (2006) J. Phys. A , vol.39 , pp. 10405-10414
    • Cassanas, R.1    Siedentop, H.2
  • 6
    • 0002569095 scopus 로고
    • The maximum mass of ideal white dwarfs
    • Chandrasekhar S. (1931). The maximum mass of ideal white dwarfs. Astrophys. J. 74: 81-82
    • (1931) Astrophys. J. , vol.74 , pp. 81-82
    • Chandrasekhar, S.1
  • 7
    • 0001564054 scopus 로고
    • An uncertainty principle for Fermions with generalized kinetic energy
    • Daubechies I. (1983). An uncertainty principle for Fermions with generalized kinetic energy. Commun. Math. Phys. 90: 511-520
    • (1983) Commun. Math. Phys. , vol.90 , pp. 511-520
    • Daubechies, I.1
  • 8
    • 0002976168 scopus 로고
    • Heat kernels and spectral theory
    • Cambridge: Cambridge University Press
    • Davies, E.B.: Heat kernels and spectral theory, Volume 92 of Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press, 1990
    • (1990) Cambridge Tracts in Mathematics , vol.92
    • Davies, E.B.1
  • 9
    • 0242704181 scopus 로고
    • Semiclassical theory of atoms
    • Berlin: Springer-Verlag
    • Englert, B.-G.: Semiclassical Theory of Atoms. Number 300 in Lecture Notes in Physics, 1 edition, Berlin: Springer-Verlag, 1988
    • (1988) Lecture Notes in Physics, 1 Edition , Issue.300
    • Englert, B.-G.1
  • 10
    • 18444372708 scopus 로고
    • Statistical atom: Handling the strongly bound electrons
    • 5
    • Englert B.-G. and Schwinger J. (1984). Statistical atom: Handling the strongly bound electrons. Phys. Rev. A 29(5): 2331-2338
    • (1984) Phys. Rev. A , vol.29 , pp. 2331-2338
    • Englert, B.-G.1    Schwinger, J.2
  • 11
    • 0040253595 scopus 로고
    • Statistical atom: Some quantum improvements
    • 5
    • Englert B.-G. and Schwinger J. (1984). Statistical atom: Some quantum improvements. Phys. Rev. A 29(5): 2339-2352
    • (1984) Phys. Rev. A , vol.29 , pp. 2339-2352
    • Englert, B.-G.1    Schwinger, J.2
  • 12
    • 0010250715 scopus 로고
    • Atomic-binding-energy oscillations
    • Englert B.-G. and Schwinger J. (1985). Atomic-binding-energy oscillations. Phys. Rev. A 32: 47-63
    • (1985) Phys. Rev. A , vol.32 , pp. 47-63
    • Englert, B.-G.1    Schwinger, J.2
  • 13
    • 0002438624 scopus 로고
    • Eigenfunctions and eigenvalues of ordinary differential operators
    • 2
    • Fefferman C. and Seco L. (1992). Eigenfunctions and eigenvalues of ordinary differential operators. Adv. Math. 95(2): 145-305
    • (1992) Adv. Math. , vol.95 , pp. 145-305
    • Fefferman, C.1    Seco, L.2
  • 14
    • 0000184899 scopus 로고
    • The density of a one-dimensional potential
    • 2
    • Fefferman C. and Seco L. (1994). The density of a one-dimensional potential. Adv. Math. 107(2): 187-364
    • (1994) Adv. Math. , vol.107 , pp. 187-364
    • Fefferman, C.1    Seco, L.2
  • 15
    • 0000104864 scopus 로고
    • The eigenvalue sum of a one-dimensional potential
    • 2
    • Fefferman C. and Seco L. (1994). The eigenvalue sum of a one-dimensional potential. Adv. Math. 108(2): 263-335
    • (1994) Adv. Math. , vol.108 , pp. 263-335
    • Fefferman, C.1    Seco, L.2
  • 16
    • 0002282644 scopus 로고
    • On the Dirac and Schwinger corrections to the ground-state energy of an atom
    • 1
    • Fefferman C. and Seco L. (1994). On the Dirac and Schwinger corrections to the ground-state energy of an atom. Adv. Math. 107(1): 1-188
    • (1994) Adv. Math. , vol.107 , pp. 1-188
    • Fefferman, C.1    Seco, L.2
  • 17
    • 0000483185 scopus 로고
    • The density in a three-dimensional radial potential
    • 1
    • Fefferman C. and Seco L. (1995). The density in a three-dimensional radial potential. Adv. Math. 111(1): 88-161
    • (1995) Adv. Math. , vol.111 , pp. 88-161
    • Fefferman, C.1    Seco, L.2
  • 18
    • 33746926232 scopus 로고
    • An upper bound for the number of electrons in a large ion
    • Fefferman C.L. and Seco L.A. (1989). An upper bound for the number of electrons in a large ion. Proc. Nat. Acad. Sci. USA 86: 3464-3465
    • (1989) Proc. Nat. Acad. Sci. USA , vol.86 , pp. 3464-3465
    • Fefferman, C.L.1    Seco, L.A.2
  • 19
    • 34249956746 scopus 로고
    • Asymptotic neutrality of large ions
    • Fefferman C.L. and Seco L.A. (1990). Asymptotic neutrality of large ions. Commun. Math. Phys. 128: 109-130
    • (1990) Commun. Math. Phys. , vol.128 , pp. 109-130
    • Fefferman, C.L.1    Seco, L.A.2
  • 20
    • 84968518113 scopus 로고
    • On the energy of a large atom
    • 2
    • Fefferman C.L. and Seco L.A. (1990). On the energy of a large atom. Bull. AMS 23(2): 525-530
    • (1990) Bull. AMS , vol.23 , pp. 525-530
    • Fefferman, C.L.1    Seco, L.A.2
  • 21
    • 0001014192 scopus 로고
    • Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential
    • 3
    • Fefferman C.L. and Seco L.A. (1993). Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential. Rev. Math. Iberoamer. 9(3): 409-551
    • (1993) Rev. Math. Iberoamer. , vol.9 , pp. 409-551
    • Fefferman, C.L.1    Seco, L.A.2
  • 23
    • 33846238566 scopus 로고
    • Eine statistische Begründung zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendungen auf die Theorie des periodischen Systems der Elemente
    • Fermi E. (1928). Eine statistische Begründung zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendungen auf die Theorie des periodischen Systems der Elemente. Z. Phys. 48: 73-79
    • (1928) Z. Phys. , vol.48 , pp. 73-79
    • Fermi, E.1
  • 24
    • 55349101942 scopus 로고    scopus 로고
    • Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
    • (in press). DOI 10.1090/s0894-0347-07-00582-6
    • Frank, R.L., Lieb, E.H., Seiringer, R.: Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. J. AMS (in press). DOI 10.1090/s0894-0347-07-00582-6
    • J. AMS
    • Frank, R.L.1    Lieb, E.H.2    Seiringer, R.3
  • 27
    • 0007331820 scopus 로고
    • An atomic lower bound that agrees with Scott's correction
    • Hughes W. (1990). An atomic lower bound that agrees with Scott's correction. Adv. in Math. 79: 213-270
    • (1990) Adv. in Math. , vol.79 , pp. 213-270
    • Hughes, W.1
  • 29
    • 0001745291 scopus 로고
    • Asymptotics of the ground state energies of large Coulomb systems
    • 2
    • Ivrii V.Ja. and Sigal I.M. (1993). Asymptotics of the ground state energies of large Coulomb systems. Ann. of Math. 138(2): 243-335
    • (1993) Ann. of Math. , vol.138 , pp. 243-335
    • Ivrii, V.Ja.1    Sigal, I.M.2
  • 30
    • 38749100675 scopus 로고    scopus 로고
    • Heavy atoms in a superstrong magnetic field
    • Providence, RI: Amer. Math. Soc.
    • Ivrii, V.: Heavy atoms in a superstrong magnetic field. In: Differential operators and spectral theory, Providence, RI: Amer. Math. Soc., 1999, pp.125-137
    • (1999) Differential Operators and Spectral Theory , pp. 125-137
    • Ivrii, V.1
  • 31
    • 28344449070 scopus 로고
    • Über die Awendbarkeit der statistischen Methode auf Ionengitter
    • Lenz W. (1932). Über die Awendbarkeit der statistischen Methode auf Ionengitter. Z. Phys. 77: 713-721
    • (1932) Z. Phys. , vol.77 , pp. 713-721
    • Lenz, W.1
  • 32
    • 0011609035 scopus 로고
    • A lower bound for Coulomb energies
    • Lieb E.H. (1979). A lower bound for Coulomb energies. Phys. Lett. 70: 444-446
    • (1979) Phys. Lett. , vol.70 , pp. 444-446
    • Lieb, E.H.1
  • 33
    • 0000681089 scopus 로고
    • Variational principle for Many-Fermion systems
    • Erratum: Phys. Rev. Lett. 47, 69 (1981)
    • Lieb, E.H.: Variational principle for Many-Fermion systems. Phys. Rev. Lett. 46, 457-459 (1981), Erratum: Phys. Rev. Lett. 47, 69 (1981)
    • (1981) Phys. Rev. Lett. , vol.46 , pp. 457-459
    • Lieb, E.H.1
  • 34
    • 33847043281 scopus 로고
    • Thomas-Fermi and related theories of atoms and molecules
    • 4
    • Lieb E.H. (1981). Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys. 53(4): 603-641
    • (1981) Rev. Mod. Phys. , vol.53 , pp. 603-641
    • Lieb, E.H.1
  • 36
    • 84983920937 scopus 로고
    • Improved lower bound on the indirect Coulomb energy
    • Lieb E.H. and Oxford S. (1981). Improved lower bound on the indirect Coulomb energy. Intern. J. Quantum Chem. 19: 427-439
    • (1981) Intern. J. Quantum Chem. , vol.19 , pp. 427-439
    • Lieb, E.H.1    Oxford, S.2
  • 37
    • 33846040104 scopus 로고
    • The Thomas-Fermi theory of atoms, molecules and solids
    • Lieb E.H. and Simon B. (1977). The Thomas-Fermi theory of atoms, molecules and solids. Adv. Math. 23: 22-116
    • (1977) Adv. Math. , vol.23 , pp. 22-116
    • Lieb, E.H.1    Simon, B.2
  • 38
    • 0002667676 scopus 로고
    • The stability and instability of relativistic matter
    • Lieb E.H. and Yau H.-T. (1988). The stability and instability of relativistic matter. Commun. Math. Phys. 118: 177-213
    • (1988) Commun. Math. Phys. , vol.118 , pp. 177-213
    • Lieb, E.H.1    Yau, H.-T.2
  • 41
    • 0034347249 scopus 로고    scopus 로고
    • On the asymptotic exactness of Thomas-Fermi theory in the thermodynamic limit
    • 2
    • Matesanz P.B. and Solovej J.P. (2000). On the asymptotic exactness of Thomas-Fermi theory in the thermodynamic limit. Ann. Henri Poincaré 1(2): 281-306
    • (2000) Ann. Henri Poincaré , vol.1 , pp. 281-306
    • Matesanz, P.B.1    Solovej, J.P.2
  • 42
    • 0004007405 scopus 로고
    • Cambridge, MA: Harvard Univ. Press Reprinting of the third edition (1726) with variant readings, Assembled and edited by A. Koyré, I.B. Cohen with the assistance of A. Whitman
    • Newton, I.: Philosophiae naturalis principia mathematica. Vol. I. Cambridge, MA: Harvard Univ. Press, 1972. Reprinting of the third edition (1726) with variant readings, Assembled and edited by A. Koyré, I.B. Cohen with the assistance of A. Whitman
    • (1972) Philosophiae Naturalis Principia Mathematica , vol.1
    • Newton, I.1
  • 44
    • 38749115918 scopus 로고    scopus 로고
    • PhD thesis, Aarhus Universitet October
    • Sørensen, T.∅.: Towards a Relativistic Scott Correction. PhD thesis, Aarhus Universitet, http://www.imf.au.dk/cgi-bin/viewers/ viewpublications.cgi?id=79, October 1998
    • (1998) Towards A Relativistic Scott Correction
    • Sørensen, T.1
  • 45
    • 18844420251 scopus 로고    scopus 로고
    • The large-Z behavior of pseudorelativistic atoms
    • 5
    • Sørensen T.∅. (2005). The large-Z behavior of pseudorelativistic atoms. J. Math. Phys. 46(5): 052307, 24
    • (2005) J. Math. Phys. , vol.46 , pp. 052307
    • Sørensen, T.1
  • 46
    • 0003306081 scopus 로고
    • Methods of modern mathematical physics. I
    • New York: Academic Press
    • Reed, M., Simon, B.: Methods of modern mathematical physics. I. Functional analysis. New York: Academic Press, 1972
    • (1972) Functional Analysis
    • Reed, M.1    Simon, B.2
  • 47
    • 0008118546 scopus 로고
    • Thomas-Fermi model: The leading correction
    • 5
    • Schwinger J. (1980). Thomas-Fermi model: The leading correction. Phys. Rev. A 22(5): 1827-1832
    • (1980) Phys. Rev. A , vol.22 , pp. 1827-1832
    • Schwinger, J.1
  • 48
    • 25344459622 scopus 로고
    • Thomas-Fermi model: The second correction
    • 5
    • Schwinger J. (1981). Thomas-Fermi model: The second correction. Phys. Rev. A 24(5): 2353-2361
    • (1981) Phys. Rev. A , vol.24 , pp. 2353-2361
    • Schwinger, J.1
  • 49
    • 34250106497 scopus 로고
    • On the leading energy correction for the statistical model of the atom: Interacting case
    • Siedentop H. and Weikard R. (1987). On the leading energy correction for the statistical model of the atom: Interacting case. Commun. Math. Phys. 112: 471-490
    • (1987) Commun. Math. Phys. , vol.112 , pp. 471-490
    • Siedentop, H.1    Weikard, R.2
  • 50
    • 0039624520 scopus 로고
    • Upper bound on the ground state energy of atoms that proves Scott's conjecture
    • Siedentop H. and Weikard R. (1987). Upper bound on the ground state energy of atoms that proves Scott's conjecture. Phys. Lett. A 120: 341-342
    • (1987) Phys. Lett. A , vol.120 , pp. 341-342
    • Siedentop, H.1    Weikard, R.2
  • 51
    • 84956073261 scopus 로고
    • On the leading energy correction of the statistical atom: Lower bound
    • Siedentop H. and Weikard R. (1988). On the leading energy correction of the statistical atom: Lower bound. Europhys. Lett. 6: 189-192
    • (1988) Europhys. Lett. , vol.6 , pp. 189-192
    • Siedentop, H.1    Weikard, R.2
  • 52
    • 34249971100 scopus 로고
    • On the leading correction of the Thomas-Fermi model: Lower bound - With an appendix by A.M.K. Müller
    • Siedentop H. and Weikard R. (1989). On the leading correction of the Thomas-Fermi model: Lower bound - with an appendix by A.M.K. Müller. Invent. Math. 97: 159-193
    • (1989) Invent. Math. , vol.97 , pp. 159-193
    • Siedentop, H.1    Weikard, R.2
  • 53
    • 0001746857 scopus 로고
    • A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators
    • 2
    • Siedentop H. and Weikard R. (1991). A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators. Ann. Sci. de l'École Normale Supér. 24(2): 215-225
    • (1991) Ann. Sci. de l'École Normale Supér. , vol.24 , pp. 215-225
    • Siedentop, H.1    Weikard, R.2
  • 54
    • 33847646155 scopus 로고    scopus 로고
    • Trace ideals and their applications
    • Providence, RI: Amer. Math. Soc.
    • Simon, B.: Trace ideals and their applications, Volume 120 of Mathematical Surveys and Monographs, 2nd ed. Providence, RI: Amer. Math. Soc., 2005
    • (2005) Mathematical Surveys and Monographs, 2nd Ed. , vol.120
    • Simon, B.1
  • 55
    • 33846410438 scopus 로고
    • A simplification of the Hartree-Fock method
    • 3
    • Slater J.C. (1951). A simplification of the Hartree-Fock method. Phys. Rev. 81(3): 385-390
    • (1951) Phys. Rev. , vol.81 , pp. 385-390
    • Slater, J.C.1
  • 56
    • 84974001842 scopus 로고
    • The quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a strong homogeneous magnetic field
    • 2
    • Sobolev A.V. (1994). The quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a strong homogeneous magnetic field. Duke Math. J. 74(2): 319-429
    • (1994) Duke Math. J. , vol.74 , pp. 319-429
    • Sobolev, A.V.1
  • 57
    • 77952509323 scopus 로고    scopus 로고
    • The relativistic Scott correction
    • M.J. Esteban, C. Le Bris, G. Scuseria, eds. Volume 47/2006 of Oberwolfach Report, Mathematisches Forschungsinstitut Oberwolfach, Berlin: European Mathematical Society
    • Solovej, J.P.: The relativistic Scott correction. In: M.J. Esteban, C. Le Bris, G. Scuseria, eds. Mathematical and Numerical Aspects of Quantum Chemistry Problems, Volume 47/2006 of Oberwolfach Report, Mathematisches Forschungsinstitut Oberwolfach, Berlin: European Mathematical Society, 2006, pp. 52-53
    • (2006) Mathematical and Numerical Aspects of Quantum Chemistry Problems , pp. 52-53
    • Solovej, J.P.1
  • 58
    • 38749129392 scopus 로고    scopus 로고
    • New coherent states and a new proof of the Scott correction
    • Advances in differential equations and mathematical physics (Birmingham, AL, 2002) Providence, RI: Amer. Math. Soc.
    • Solovej, J.P., Spitzer, W.L.: New coherent states and a new proof of the Scott correction. In: Advances in differential equations and mathematical physics (Birmingham, AL, 2002), Volume 327 of Contemp. Math., Providence, RI: Amer. Math. Soc., 2003, pp. 305-319
    • (2003) Contemp. Math. , vol.327 , pp. 305-319
    • Solovej, J.P.1    Spitzer, W.L.2
  • 59
    • 0242593273 scopus 로고    scopus 로고
    • A new coherent states approach to semiclassics which gives Scott's correction
    • 2-3
    • Solovej J.P. and Spitzer W.L. (2003). A new coherent states approach to semiclassics which gives Scott's correction. Commun. Math. Phys. 241(2-3): 383-420
    • (2003) Commun. Math. Phys. , vol.241 , pp. 383-420
    • Solovej, J.P.1    Spitzer, W.L.2
  • 60
    • 0011365987 scopus 로고
    • A lower bound with the best possible constant for Coulomb Hamiltonians
    • Thirring W. (1981). A lower bound with the best possible constant for Coulomb Hamiltonians. Commun. Math. Phys. 79: 1-7
    • (1981) Commun. Math. Phys. , vol.79 , pp. 1-7
    • Thirring, W.1
  • 61
    • 84937022828 scopus 로고
    • The calculation of atomic fields
    • Thomas L.H. (1927). The calculation of atomic fields. Proc. Camb. Phil. Soc. 23: 542-548
    • (1927) Proc. Camb. Phil. Soc. , vol.23 , pp. 542-548
    • Thomas, L.H.1
  • 62
    • 0040568178 scopus 로고
    • Spectral analysis of pseudodifferential operators
    • Weder R. (1975). Spectral analysis of pseudodifferential operators. J. Funct. Anal. 20: 319-337
    • (1975) J. Funct. Anal. , vol.20 , pp. 319-337
    • Weder, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.