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Density Functional Methods In Physics pp 81–140Cite as

Density Functional Approach to Time-Dependent and to Relativistic Systems

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Part of the book series: NATO ASI Series ((ASIB,volume 123))

Abstract

Density functional methods, in general, can be discussed on three different levels. The first is the level of fundamental1,2 existence theorems such as those of Hohenberg, Kohn and Sham (HKS) and related mathematical topics. The second level consists of the various approaches 2–32 to a systematic construction of density functionals. Prominent among these are the different gradient expansion techniques. The approximations required on this level depend, of course, on the particular situation to be described. The third level consists of practical schemes and numerical solutions for real physical systems.

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References

  1. P. Hohenberg and W. Kohn, Phys. Rev. 136: B864 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  2. W. Kohn and L.J. Sham, Phys. Rev. 140: A1133 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  3. L.J. Sham and W. Kohn, Phys. Rev. 145: 561 (1966).

    Article  ADS  Google Scholar 

  4. G.A. Baraff and S. Borowitz, Phys. Rev. 121:1704 (1961).

    Article  MathSciNet  ADS  Google Scholar 

  5. S.-K.Ma and K.A. Brueckner, Phys. Rev. 165:18 (1968).

    Article  ADS  Google Scholar 

  6. L.J. Sham, in “Computational Methods in Band Structure,”p.458, P.M. Marcus, J.F. Janak, and A.R. Williams, eds., Plenum, New York (1971).

    Google Scholar 

  7. E.K.U. Gross and R.M. Dreizler, Z. Phys. A302: 103 (1981).

    Article  ADS  Google Scholar 

  8. D.J.W. Geldart and M. Rasolt, Phys. Rev. B13:1477 (1976).

    Article  ADS  Google Scholar 

  9. D.C. Langreth and J.P. Perdew, Phys. Rev. B21:5469 (1980).

    Article  ADS  Google Scholar 

  10. V. Sahni, J. Gruenebaum, and J.P. Perdew, Phys. Rev. B26:4371 (1982).

    Article  ADS  Google Scholar 

  11. J.C. Stoddart, A.M. Beattie, and N.H. March, Int. J. Quant.Chem. 4:35 (1971).

    Google Scholar 

  12. A.M. Beattie, J.C. Stoddart, and N.H. March, Proc. Roy. Soc. A326:97 (1971).

    Article  ADS  Google Scholar 

  13. O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B13:4274 (1975).

    ADS  Google Scholar 

  14. O. Gunnarsson, M. Jonson and B.I. Lundqvist, Phys. Lett. 59A:177 (1976).

    Article  ADS  Google Scholar 

  15. O. Gunnarsson, M. Jonson, and B.I. Lundqvist, Solid State Comm. 24:765 (1977).

    Article  ADS  Google Scholar 

  16. D.A. Kirzhnits, “Field Theoretical Methods in Many-Body Systems,” Pergamon, Oxford (1967).

    Google Scholar 

  17. C.H. Hodges, Can. J. Phys. 51:1428 (1973).

    Article  ADS  Google Scholar 

  18. D.R. Murphy, Phys. Rev. 24:1682 (1981).

    Article  ADS  Google Scholar 

  19. B. Grammaticos and A. Voros, Ann. Phys. 123: 359 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  20. S.F.J. Wilk, Y. Fujiwara, and T.A. Osborn, Phys. Rev. A24:2187 (1981).

    MathSciNet  ADS  Google Scholar 

  21. Y. Fujiwara, T.A. Osborn, and S.F.J. Wilk, Phys. Rev. A25: 14 (1982).

    Google Scholar 

  22. E. Tirapegui, F. Langouche, and D. Roekaerts, Phys. Rev. A27:2649 (1982).

    MathSciNet  ADS  Google Scholar 

  23. V. Peuckert, J. Phys. C7: 2221 (1974).

    ADS  Google Scholar 

  24. V. Peuckert, J. Phys. C9: 809 (1976).

    ADS  Google Scholar 

  25. V. Peuckert, J. Phys. C9: 4173 (1976).

    ADS  Google Scholar 

  26. C.Q. Ma and V. Sahni, Phys. Rev. B16: 4249 (1977).

    Article  ADS  Google Scholar 

  27. U. von Barth and L. Hedin, J. Phys. C5: 1629 (1972).

    Google Scholar 

  28. G.L. Oliver and J.P. Perdew, Phys. Rev. A20:397 (1979).

    Article  ADS  Google Scholar 

  29. L. Fritsche and H. Gollisch, in: “Local Density Approximations in Quantum Chemistry and Solid State Physics,” J.P. Dahl and J. Avery, eds., Plenum, New York (1984).

    Google Scholar 

  30. G.E.W. Bauer, Phys. Rev. B27: 5912 (1983).

    Article  ADS  Google Scholar 

  31. K.F. Freed and M. Levy, J. Chem. Phys. 77:396 (1982).

    Article  ADS  Google Scholar 

  32. G. Zumbach and K. Maschke, Phys. Rev. A28:544 (1983).

    MathSciNet  ADS  Google Scholar 

  33. E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52:997 (1984).

    Article  ADS  Google Scholar 

  34. E.K.U. Gross and R.M. Dreizler, Phys. Rev. A20:1798 (1979).

    Google Scholar 

  35. W. Stich, E.K.U. Gross, P. Malzacher, and R.M. Dreizler, Z. Phys. A309: 5 (1982).

    Article  ADS  Google Scholar 

  36. E.K.U. Gross, A. Toepfer, B. Jacob, and R.M. Dreizier, in: “Proceedings of the XVII International Winter Meeting on Nuclear Physics in Bormio 1979,” p. 68–94, I. Iori, ed., Instituto Nazionale di Fisica Nucleare, Milano (1979)

    Google Scholar 

  37. R.M. Dreizier, E.K.U. Gross, and A. Toepfer, Phys. Lett. 71A: 49 (1979).

    Article  ADS  Google Scholar 

  38. A. Toepfer, E.K.U. Gross, and R.M. Dreizier, Phys. Rev. A20: 1808 (1979).

    Article  ADS  Google Scholar 

  39. A. Toepfer, E.K.U. Gross, and R.M. Dreizler, Z. Phys. A298: 167 (1980).

    Article  ADS  Google Scholar 

  40. E.K.U. Gross and J. Rafeiski, Phys. Rev. A20:44 (1979).

    Article  ADS  Google Scholar 

  41. R.M. Dreizler, E.K.U. Gross, M. Horbatsch, B. Jacob, H.J. Lüdde, and A. Toepfer, in:“ Proceedings of the XVIII International Winter Meeting on Nuclear Physics in Bormio 1980,” p.764–794, RicercaScientifica ed Educazione Permanente, supplemento n.13, Milano (1980).

    Google Scholar 

  42. E.K.U. Gross and R.M. Dreizler, Phys. Lett. 81A:447 (1981).

    Google Scholar 

  43. R.M. Dreizier and E.K.U. Gross, in:“ Quantum Electrodynamics of Strong Fields,” p. 383–412, W. Greiner, ed., Plenum, New York (1983).

    Google Scholar 

  44. E.K.U. Gross and R.M. Dreizler, in:“ Local Density Approxi- mations in Quantum Chemistry and Solid State Physics,” p. 353–380, J.P. Dahl and J. Avery, eds., Plenum, New York (1984).

    Google Scholar 

  45. M. Horbatsch and R.M. Dreizler, Z. Phys.A300:119 (1981).

    Google Scholar 

  46. M. Horbatsch and R.M. Dreizier, Z.Phys. A308:329 (1982).

    Article  ADS  Google Scholar 

  47. H.J. Lüdde, M. Horbatsch, E.K.U. Gross, and R.M. Dreizler, in: “Proceedings of the XVII International Winter Meeting on Nuclear Physics in Bormio 1979,” p. 120–136, I. Iori, ed., Instituto Nazionale di Fisica Nucleare, Milano (1979).

    Google Scholar 

  48. M. Horbatsch, H.J. Lüdde, A. Henne, E.K.U. Gross, and R.M. Dreizler, in:“ XII International Conference on the Physics of Electronic and Atomic Collisions (Gatlinburg, Tennessee, 1981), Abstracts of Contributed Papers I,” p. 545–546, S. Datz, ed., Oak Ridge (1981).

    Google Scholar 

  49. G. Holzwarth, Phys. Lett. B66:29 (1977).

    Article  ADS  Google Scholar 

  50. G. Holzwarth, Phys. Rev. C16: 885 (1977).

    ADS  Google Scholar 

  51. For a similar treatment of nuclear giant resonances, see G. Holzwarth, this volume.

    Google Scholar 

  52. P. Malzacher and R.M. Dreizler, Z. Phys. A307: 211 (1982).

    Article  ADS  Google Scholar 

  53. S.C. Ying, Nuovo Cim. 23B: 270 (1974).

    Article  ADS  Google Scholar 

  54. G. Mukhopadhyay and S. Lundqvist, Nuovo Cim. 27B: 1 (1975).

    Article  ADS  Google Scholar 

  55. L.J. Bartolotti, Phys. Rev.A24:1661 (1981); ibid. A26: 2243 (1982).

    Google Scholar 

  56. M. Levy, Proc. Natl. Acad. Sci. USA 76: 6062 (1979).

    Article  ADS  Google Scholar 

  57. V. Peuckert, J. Phys. C11: 4945 (1978).

    ADS  Google Scholar 

  58. L.H. Thomas, Proc. Camb. Phil. Soc. 23:542 (1926).

    Article  ADS  Google Scholar 

  59. E. Fermi, Rend. Acad. Naz. Linzei 6:602 (1927).

    Google Scholar 

  60. P.A.M. Dirac, Proc. Camb. Phil. Soc. 26:376 (1930).

    Article  ADS  MATH  Google Scholar 

  61. C.F.v.Weizsäcker,Z. Phys. 96: 431 (1935).

    Article  Google Scholar 

  62. C. Schweitzer, R.M. Dreizler, and E.K.U. Gross, to be published.

    Google Scholar 

  63. F. Herman, J.P. Van Dyke, and I.B. Ortenburger, Phys. Rev. Lett. 22:807 (1969).

    Article  ADS  Google Scholar 

  64. L. Kleinman, Phys. Rev. B10: 2221 (1974).

    Article  ADS  Google Scholar 

  65. D.J.W. Geldart, M. Rasolt, and C.O. Almbladh, Solid State Comm. 16: 243 (1975).

    Article  ADS  Google Scholar 

  66. R. Latter, Phys. Rev. 99:510 (1955).

    Article  ADS  Google Scholar 

  67. S.B. Schneiderman and A. Russek, Phys. Rev. 181:311 (1969).

    Article  ADS  Google Scholar 

  68. K. Taulbjerg, J. Vaaben, and B. Fastrup, Phys. Rev. Al2:2325 (1975).

    Article  ADS  Google Scholar 

  69. R.M. Dreizler, in:“ Critical Phenomena in Heavy Ion Physics (Brasov International School 1980),” p.205–257, A.A. Raduta and G. Stratan,eds., Central Institute of Physics, Bucharest (1980).

    Google Scholar 

  70. E. Clementi and C. Roetti, At. Data Nucl. Data Tab. 14:177 (1974).

    Google Scholar 

  71. J. Scott, Phil. Mag. 43: 859 (1952).

    Google Scholar 

  72. J. Schwinger, Phys. Rev. A22:1827 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  73. E. Lieb, Rev. Mod. Phys. 53:603 (1981).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  74. J.P. Desclaux, At. Data Nucl. Data Tab. 12:311 (1973).

    Article  ADS  Google Scholar 

  75. W.C. Ermler, R.S. Mulliken, and A.C. Wahl, J. Chem. Phys. 66:30–31 (1977).

    Google Scholar 

  76. J. Eichler and U. Wille, Phys. Rev. A11: 1973 (1975).

    Article  ADS  Google Scholar 

  77. A. Toepfer, B. Jacob, H.J. Lüdde, and R.M. Dreizier, Phys. Lett. 93A:18 (1982).

    Google Scholar 

  78. A. Toepfer, B. Jacob, H.J. Lüdde, and R.M. Dreizier, Z. Phys.

    Google Scholar 

  79. T. Andersen, E. Beaving, P. Hedegard, and 0.J. Ostgard, J. Phys. B11: 1449 (1978).

    ADS  Google Scholar 

  80. R. Hippler and K.-H. Schartner, J. Phys. B8:25–28 (1975).

    Google Scholar 

  81. For a broad review, see M.V. Ramana and A.K. Rajagopal, Adv. Chem. Phys. 54:231 (1983).

    Google Scholar 

  82. A.K. Rajagopal, this volume.

    Google Scholar 

  83. M.S. Vallarta and N. Rosen, Phys. Rev. 41: 708 (1932).

    Article  ADS  MATH  Google Scholar 

  84. H. Jensen, Z. Phys. 82: 794 (1933).

    Article  ADS  Google Scholar 

  85. N. Ashby and M.A. Holzman, Phys. Rev. A1:764 (1970).

    Google Scholar 

  86. M. Rudkjqcbing, Kgl. Danske Videnskab Selskab, Mat.-Fys. Med. 27, No. 5 (1952).

    Google Scholar 

  87. B. Jancovici, Nuovo Cim. 25: 428 (1962).

    Article  MATH  Google Scholar 

  88. E.E. Salpeter, Astrophys. J. 134:669 (1961).

    ADS  Google Scholar 

  89. F. Constantinescu, “ Distributionen und ihre Anwendungen in der Physik,” p. 59 ff, Teubner, Stuttgart (1974).

    Book  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Frankfurt, D-6000, Frankfurt am Main, Federal Republic of Germany

    Eberhard K. U. Gross & Reiner M. Dreizler

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  1. Eberhard K. U. Gross
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  2. Reiner M. Dreizler
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Editors and Affiliations

  1. Institute for Theoretical Physics, Johann Wolfgang Goethe University, Frankfurt/Main, Federal Republic of Germany

    Reiner M. Dreizler

  2. Department of Physics, University of Coimbra, Coimbra, Portugal

    João da Providência

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© 1985 Plenum Press, New York

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Gross, E.K.U., Dreizler, R.M. (1985). Density Functional Approach to Time-Dependent and to Relativistic Systems. In: Dreizler, R.M., da Providência, J. (eds) Density Functional Methods In Physics. NATO ASI Series, vol 123. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0818-9_4

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  • DOI: https://doi.org/10.1007/978-1-4757-0818-9_4

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