Many-Body Problems

  • Daniel R. Bes
Chapter
Part of the Graduate Texts in Physics book series (GTP)

Abstract

So far, we have discussed only one-particle problems. We now turn our attention to cases in which more than one particle is present.

Keywords

Landau Level Einstein Condensation Extended State Closed Shell Identical Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    B.C. Olschak: Buthan. Land of Hidden Treasures. Photography by U. and A. Gansser (Stein & Day, New York 1971).Google Scholar
  2. 2.
    M. Planck: Verh. Deutsch. Phys. Ges. 2, 207, 237 (1900).Google Scholar
  3. 3.
    A. Einstein: Ann. der Phys. 17, 132 (1905).Google Scholar
  4. 4.
    A.H. Compton: Phys. Rev. 21, 483 (1923).Google Scholar
  5. 5.
    C.L. Davisson and L.H. Germer: Nature 119, 528 (1927); G.P. Thomson: Proc. Roy. Soc. A 117, 600 (1928).Google Scholar
  6. 6.
    H. Geiger and E. Mardsen: Proc. Roy. Soc. A 82, 495 (1909); E. Rutherford: Phil. Mag. 21, 669 (1911).Google Scholar
  7. 7.
    J. Balmer: Verh. Naturf. Ges. Basel 7, 548, 750 (1885); Ann. der Phys. und Chem. 25, 80 (1885).Google Scholar
  8. 8.
    N. Bohr: Phil. Mag. 25, 10 (1913); 26, 1 (1913); Nature 92, 231 (1913).Google Scholar
  9. 9.
    W. Heisenberg: Zeitschr. Phys. 33, 879 (1925).Google Scholar
  10. 10.
    M. Born, W. Heisenberg and P. Jordan: Zeitschr. Phys. 35, 557 (1926).Google Scholar
  11. 11.
    P.A.M. Dirac: Proc. Roy. Soc. A 109, 642 (1925).Google Scholar
  12. 12.
    E. Schrödinger: Ann. der Phys. 79, 361, 489 (1926); 80, 437 (1926); 81, 109 (1926).Google Scholar
  13. 13.
    D.F. Styer et al.: Am J. Phys. 70, 288 (2002).Google Scholar
  14. 14.
    J. Schwinger: Quantum Mechanics. Symbolism of Atomic Measurements, ed. by B.G Englert (Springer-Verlag, Berlin, Heidelberg, New York 2001) Chap. 1.Google Scholar
  15. 15.
    P.A.M. Dirac: The Principles of Quantum Mechanics (Oxford University Press, Amen House, London 1930).Google Scholar
  16. 16.
    A. Einstein, B. Podolsky and N. Rosen: Phys. Rev. 47, 777 (1935).Google Scholar
  17. 17.
    O. Stern and W. Gerlach: Zeitschr. Phys. 8, 110 (1921); 9, 349 (1922).Google Scholar
  18. 18.
    G. Kaiser: J. Math. Phys. 22, 705 (1981).Google Scholar
  19. 19.
    D.F. Styer: Am. J. Phys. 64, 31 (1996).Google Scholar
  20. 20.
    J. Roederer: Information and its Role in Nature (Springer-Verlag, Berlin, Heidelberg, New York 2005).Google Scholar
  21. 21.
    N. Bohr: The Philosophical Writings of Niels Bohr (Ox Bow Press, Woodbridge, Connecticut 1987).Google Scholar
  22. 22.
    N.D. Mermin: Am. J. Phys. 71, 23 (2003).Google Scholar
  23. 23.
    R.F. Feynman, R.B. Leighton and M. Sands: The Feynman Lectures on Physics. Quantum Mechanics [Addison-Wesley, Reading (Massachusetts), London, New York, Dallas, Atlanta, Barrington (Illinois) 1965] Chap. 5.Google Scholar
  24. 24.
    A. Zeilinger, R. Gähler, C.G. Shull, W. Treimer and W. Hampe: Rev. Mod. Phys. 60, 1067 (1988).Google Scholar
  25. 25.
    O. Nairz, M. Arndt and A. Zeilinger: Am. J. Phys. 71, 319 (2003).Google Scholar
  26. 26.
    W. Heisenberg: Zeitschr. Phys. 43, 172 (1927).Google Scholar
  27. 27.
    B. Cougnet, J. Roederer and P. Waloshek: Z. für Naturforschung A 7, 201 (1952).Google Scholar
  28. 28.
    W. Wootters and W. Zurek: Nature 299, 802 (1982); Phys. Today, 76 (Feb. 2009).Google Scholar
  29. 29.
    R.S. Mulliken: Nature 114, 350 (1924).Google Scholar
  30. 30.
    E.T. Jaynes and F.W. Cummings: Proc. I.E.E.E. 51, 81 (1963).Google Scholar
  31. 31.
    M. Born: Zeitschr. Phys. 37, 863 (1926); 38, 499 (1926).Google Scholar
  32. 32.
    L. de Broglie: C. R. Acad. Sci. Paris 177, 507, 548 (1923).Google Scholar
  33. 33.
    G. Binning and H. Rohrer: Rev. Mod. Phys. 71, S324 (1999) and references contained therein.Google Scholar
  34. 34.
    F. Bloch: Zeitschr. Phys. 52, 555 (1928).Google Scholar
  35. 35.
    G.E. Uhlenbeck and S.A. Goudsmit: Nature 113, 953 (1925); 117, 264 (1926).Google Scholar
  36. 36.
    W. Pauli: Zeitschr. Phys. 43, 601 (1927).Google Scholar
  37. 37.
    S. Haroche and J.M. Raimond: Exploring the Quantum. Atoms, Cavities and Photons (Oxford University Press, Oxford (2010).Google Scholar
  38. 38.
    Å. Bohr and B. Mottelson: Nuclear Structure (W.A. Benjamin, New York, Amsterdam 1969)Google Scholar
  39. 39.
    R.P. Martinez–y–Romero, H.N. Nuñez–Yepez and A.L. Salas–Brito: Am. J. Phys. 75, 629 (2007).Google Scholar
  40. 40.
    A.K. Grant and J.L. Rosner: Am. J. Phys. 62, 310 (1994).Google Scholar
  41. 41.
    D.A. McQuarrie: Quantum Chemistry (University Science Books, Herndon, Virginia 1983) Fig. 6-12.Google Scholar
  42. 42.
    W. Pauli: Zeitschr. Phys. 31, 625 (1925).Google Scholar
  43. 43.
    K.L. Jones et al.: Nature 465, 454 (2010).Google Scholar
  44. 44.
    M. Kastner: Physics Today 46, 24 (1993).Google Scholar
  45. 45.
    R. Fitzgerald: Physics Today 57, 22 (2004) and references contained therein.Google Scholar
  46. 46.
    A. Einstein: Sitz. Ber. Preuss. Ak. Wiss. 2, 261 (1924); 3 (1925).Google Scholar
  47. 47.
    D. Kleppner: Physics Today 49, 11 (1996); F. Dalfovo, S. Giorgini, L.P. Pitaevckii and S. Stringari: Rev. Mod. Phys. 71, 463 (1999).Google Scholar
  48. 48.
    M.H. Anderson, J.R. Enscher, M.R. Matthews, C.E. Wieman and E.A. Cornell: Science 269, 198 (1995); J.R. Enscher, D.S. Jin, M.R. Matthews, C.E. Wieman and E.A. Cornell: Phys. Rev. Lett. 77, 4984 (1996).Google Scholar
  49. 49.
    K. von Klitzing, G. Dorda and M. Pepper: Phys. Rev. Lett. 45, 494 (1980).Google Scholar
  50. 50.
    D.C. Tsui, H.L. Störmer and A.C. Gossard: Phys. Rev. Lett. 48, 1559 (1982); Phys. Rev. B 25, 1405 (1982).Google Scholar
  51. 51.
    R.E. Prange: Introduction to The Quantum Hall Effect, ed. by R.E. Prange and S.M. Girvin (Springer-Verlag, New York, Berlin, Heidelberg 1987) Fig. 1.2.Google Scholar
  52. 52.
    B.L. Halperin: Scientific American 254, Vol. 4, 52 (1986).Google Scholar
  53. 53.
    J.D. Jackson: Classical Electrodynamics (John Wiley & Sons, New York, Chichester, Brisbane, Toronto 1975) p. 574.Google Scholar
  54. 54.
    R.B. Laughlin: Phys. Rev. Lett. 50, 1395 (1983).Google Scholar
  55. 55.
    S.N. Bose: Zeitschr. Phys. 26, 178 (1924).Google Scholar
  56. 56.
    P.A.M. Dirac: Proc. Roy. Soc. A 112, 661 (1926).Google Scholar
  57. 57.
    E. Fermi: Zeitschr. Phys. 36, 902 (1926).Google Scholar
  58. 58.
    R. Eisberg and R. Resnick: Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (John Wiley & Sons, New York (1975).Google Scholar
  59. 59.
    R.P. Feynman: Phys. Rev. 76, 769 (1949).Google Scholar
  60. 60.
    C. Itzykson and J.B. Zuber: Quantum Field Theory (McGraw-Hill, New York, St. Louis, San Francisco, London 1980).Google Scholar
  61. 61.
    B.H. Brandow: Rev. Mod. Phys. 39, 771 (1967); E.M. Krenciglowa and T.T.S. Kuo: Nucl. Phys. A 240, 195 (1975).Google Scholar
  62. 62.
    C. Bloch and J. Horowitz: Nucl. Phys. 8, 91 (1958).Google Scholar
  63. 63.
    J.J. Sakurai: Modern Quantum Mechanics. Addison–Wesley Pub. Co., Reading, Massachusetts (1994).Google Scholar
  64. 64.
    A. Einstein: Verh. Deutsch. Phys. Ges. 18, 318 (1916); Mitt. Phys. Ges. Zürich 16, 47 (1916); Phys. Zeitschr. 18, 121 (1917).Google Scholar
  65. 65.
    T.H. Maiman: Nature 187, 493 (1960).Google Scholar
  66. 66.
    J. Bardeen, L.N. Cooper and J.R. Schrieffer: Phys. Rev. 106, 162 (1957).Google Scholar
  67. 67.
    C. Becchi, A. Rouet and R. Stora: Phys. Lett. B 52, 344 (1974).Google Scholar
  68. 68.
    M. Henneaux and C. Teitelboim: Quantization of Gauge Systems (Princeton University Press, Princeton, New Jersey 1992).Google Scholar
  69. 69.
    D.R. Bes and J. Kurchan: The Treatment of Collective Coordinates in Many-Body Systems. An Application of the BRST Invariance (World Scientific Lecture Notes in Physics, Vol. 34, Singapore, New Jersey, London, Hong Kong 1990); D.R. Bes and O. Civitarese: Am. J. Phys. 70, 548 (2002).Google Scholar
  70. 70.
    H. Kammerlingh Onnes, Comm. Phys. Lab. Univ. Leiden, Nos. 122 and 124 (1911).Google Scholar
  71. 71.
    B.D. Josephson, Phys. Lett. 1, 251 (1962).Google Scholar
  72. 72.
    R. Feynman and A. Hibbs: Quantum Mechanics and Path Integrals (Mc Graw–Hill Book Co., New York 1965).Google Scholar
  73. 73.
    P. Cartier and C. DeWitt–Morette: Functional Integration (Cambridge U. Press, New York 2007).Google Scholar
  74. 74.
    S. Carlip: Phys. Today 61, 61 (2008).Google Scholar
  75. 75.
    L.S. Schulman: Techniques and Applications of Path Integrals (John Wiley & Sons, New York 1981).Google Scholar
  76. 76.
    E. Schrödinger: Naturwissenschaften 23, 807, 823, 845 (1935)Google Scholar
  77. 77.
    A. Aspect: Introduction: John Bell and the Second Quantum Revolution, in J.S. Bell, “Speakable and Unspeakable in Quantum Mechanics”, Cambridge University Press (2008).Google Scholar
  78. 78.
    A. Zeilinger: Rev. Mod. Phys. 71, S288 (1999) and references contained thereinGoogle Scholar
  79. 79.
    A. Zeilinger, G. Weihs, T. Jennewein and M. Aspelmeyer: Nature 433, 230 (2005).Google Scholar
  80. 80.
    D. Bohm: Quantum Theory. Prentice Hall, New Jersey (1951); Phys. Rev. 85, 166, 180 (1952).Google Scholar
  81. 81.
    J.S. Bell: Physics 1, 195 (1964).Google Scholar
  82. 82.
    N.D. Mermin: Physics Today, 38 (1985).Google Scholar
  83. 83.
    A. Aspect, P. Grangier and G. Roger: Phys. Rev. Lett. 47, 460 (1981); 49, 91 (1982).Google Scholar
  84. 84.
    G. Weihs, T. Jennewein, C. Simon, H. Weinfurter and A. Zeilinger: Phys. Rev. Lett. 81, 5039 (1998).Google Scholar
  85. 85.
    W. Nagourney, J. Sandberg and H. Dehmet, Phys. Rev. Lett. 56, 2797 (1986).Google Scholar
  86. 86.
    M. Brune et al.: Phys. Rev. Lett. 76, 1800 (1996).Google Scholar
  87. 87.
    M.A. Rowe et al.: Nature 409, 791 (2001).Google Scholar
  88. 88.
    A.D. O’Connell et al.: Nature 464, 697 (2010).Google Scholar
  89. 89.
    C.H. Bennet and G. Brassard: Proc. I.E.E.E. Int. Conf. on Computers, Systems and Signal Processing (IEEE Press, Los Alamos, California 1984) p. 175.Google Scholar
  90. 90.
    C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. Wooters: Phys. Rev. Lett. 70, 1895 (1993).Google Scholar
  91. 91.
    D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger: Nature 390, 575 (1997).Google Scholar
  92. 92.
    E. Gerjuoy: Am. J. Phys. 73, 521 (2005).Google Scholar
  93. 93.
    P.W. Schor: Proc. 34th Annual Symp. Found. Comp. Scien. (FOCS), ed. by S. Goldwasser (IEEE Press, Los Alamitos, California 1994) p. 124.Google Scholar
  94. 94.
    I.L. Chuang, L.M.K. Vandersypen, X.L. Zhou, D.W. Leung and S. Lloyd: Nature 393, 143 (1998).Google Scholar
  95. 95.
    P.A.M. Dirac: Hungarian Ac. of Sc. Rep. KFK-62 (1977).Google Scholar
  96. 96.
    E. Schrödinger: Naturwissenschaftern. 23, 807, 823, 844 (1935).Google Scholar
  97. 97.
    R. Penrose: The Road to Reality (Alfred A. Knopf, New York, 2005, Chapter 29).Google Scholar
  98. 98.
    M. Schlosshauer: Decoherence and the Quantum–to–Classical Transition (Springer–Verlag, Berlin, Heidelberg 2007).Google Scholar
  99. 99.
    W.H. Zurek: Revs. Mod. Phys. 75, 715 (2003) and references contained therein; Phys. Today 49, 36 (1991).Google Scholar
  100. 100.
    J.P. Paz and W.H. Zurek: Environment-Induced Decoherence and the Transition from Classical to Quantum. In: Coherent Atomic Matter Waves, Les Houches Session LXXXII, ed. by R. Kaiser, C. Westbrook and F. Davids (Springer-Verlag, Berlin, Heidelberg, New York 2001) p. 533.Google Scholar
  101. 101.
    J. von Neumann: Matematische Grundlagen der Quantenmechanik (Springer, Berlin 1932).Google Scholar
  102. 102.
    L. Hackermüller, K. Hornberger, B. Brezger, A. Zeilinger, M. Arndt: Appl. Phys. B 77, 781 (2003)Google Scholar
  103. 103.
    E. Hobsbawn: The Age of Extremes. A History of the World, 1914–1991 (Vintage Books, New York 1996) p. 7.Google Scholar
  104. 104.
    O. Spengler: Der Untergang des Abendlandes. Umrisse einer Morphologie der Weltgeschichte, Vol. 1: Gestalt und Wirklichkeit (Munich, 1918). First English translation: The Decline of the West, Vol. 1: Form and Actuality (Knof, New York 1926).Google Scholar
  105. 105.
    H. Kragh: Quantum Generations. A History of Physics in the Twentieth Century (Princeton University Press, Princeton, New Jersey 1999).Google Scholar
  106. 106.
    A. Pais: ‘Subtle is the Lord...’ The Science and the Life of Albert Einstein (Oxford University Press, Oxford, New York, Toronto 1982). Inward Bound (Oxford University Press, Oxford, New York, Toronto 1986); Niels Bohr’s Times. In Physics, Philosophy and Politics (Clarendon Press, Oxford 1991).Google Scholar
  107. 107.
    P. Robertson: The Early Years. The Niels Bohr Institute 1921–1930 (Akademisk Forlag. Universitetsforlaget i København, Denmark 1979).Google Scholar
  108. 108.
    G. Kirchhoff: Ann. Phys. Chem. 109, 275 (1860).Google Scholar
  109. 109.
    W. Wien: Sitz. Ber. Preuss. Ak. Wiss. 55 (1893); Ann. Physik 58, 662 (1896).Google Scholar
  110. 110.
    G. Kirchhoff and R. Bunsen: Ann. Phys. Chem. 110, 160 (1860).Google Scholar
  111. 111.
    R. Millikan: Phys. Rev. 4, 73 (1914); 6, 55 (1915).Google Scholar
  112. 112.
    E. Lawrence and J. Beams: Phys. Rev. 32, 478 (1928); A. Forrester, R. Gudmundsen and P. Johnson: Phys. Rev. 90, 1691 (1955).Google Scholar
  113. 113.
    J. Clauser: Phys. Rev. D 9, 853 (1974).Google Scholar
  114. 114.
    H.G.J. Moseley: Nature 92, 554 (1913); Phil. Mag. 26, 1024 (1913); 27, 703 (1914).Google Scholar
  115. 115.
    J. Frank and H. Hertz: Verh. Deutsch. Phys. Ges. 16, 457 (1914).Google Scholar
  116. 116.
    A. Sommerfeld: Sitz. Ber. Bayer. Akad. Wiss. 459 (1915).Google Scholar
  117. 117.
    L.H. Thomas: Nature 117, 514 (1926); Phil. Mag. 3, 1 (1927).Google Scholar
  118. 118.
    M. Born and P. Jordan: Zeitschr. Phys. 34, 858 (1925).Google Scholar
  119. 119.
    W. Heisenberg: Zeitschr. Phys. 38, 499 (1926).Google Scholar
  120. 120.
    P.A.M. Dirac: Proc. Roy. Soc. A 117, 610 (1928); A 118, 351 (1928).Google Scholar
  121. 121.
    N. Bohr, H.A. Kramers and J.C. Slater: Phil. Mag. [6] 47, 785 (1924); Zeitschr. Phys. 24, 69 (1924).Google Scholar
  122. 122.
    N. Bohr: Nature 136, 65 (1935); Phys. Rev. 48, 696 (1935).Google Scholar
  123. 123.
    A. Einstein: Reply to Criticisms. In: Albert Einstein. Philosopher-Scientist, ed. by P.A Schilpp (Open Court Publishing, Peru, Illinois 2000) p. 663.Google Scholar
  124. 124.
    N. Bohr: Discussions with Einstein on Epistemological Problems in Atomic Physics. In Albert Einstein. Philosopher-Scientist, ed. by P.A Schilpp (Open Court Publishing, Peru, Illinois 2000) p. 199.Google Scholar
  125. 125.
    M. Tegmark and J.A. Wheeler: Scientific American 284, Vol. 2, 54 (2001).Google Scholar
  126. 126.
    J. Bell, Rev. Mod. Phys. 38, 447 (1966).Google Scholar
  127. 127.
    H.D. Zeh: Found. Phys. 1, 69 (1970).Google Scholar
  128. 128.
    W.H. Zurek: Phys. Rev. D 24, 1516 (1981); 26, 1862 (1982).Google Scholar
  129. 129.
    W.H. Zurek: Reduction of the Wavepacket: How Long does it take?. In: Frontiers in Nonequilibrium Statistical Mechanics, G.T. Moore and M.O. Scully, eds. (Plenum Press, New York, 1986) p.145Google Scholar
  130. 130.
    E. Joos and H.D. Zeh: Z. Phys. B: Condens. Matter 59, 223 (1985).Google Scholar
  131. 131.
    The NIST Reference on Constants, Units, and Uncertainty: Appendix 3. http:/physics.nist.gov/cuu/Units/units.html.
  132. 132.
    R.W. Richardson: Phys. Lett. 3, 277 (1963); J. Dukelsky, H.S. Lerma, L. Robledo, R. Rodriguez-Guzman and S.M. Rombouts: Phys. Rev. C 84, 061301 (2011).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Daniel R. Bes
    • 1
  1. 1.Comision Nacional de Energia AtomicaUniversidad FavaloroC.A.B.A.Argentina

Personalised recommendations