Skip to main content

Abstract

The term measurement in general means a way of determining or reading the value of a particular property associated with an individual system. In classical physics the perturbation induced by the interaction between a measured system and a measuring apparatus can be made as small as desired. In other words the principles of classical physics allow us to know the current state of a system with an arbitrarily small disturbance; this may be called noninvasive measurements in classical physics. This is not true however in quantum physics, essentially because of the following generic feature: If two systems temporarily interact, even after the interaction is over, the composite system described quantum mechanically is inevitably left in an entangled state. This means that the joint wave function is not just a product of wave functions associated with each system. This is true whatever the strength and duration of the interaction in question—even if one of the systems involved is macroscopic (in the usual sense of a system made up of a large number of microphysical constituents). For reasons discussed in this chapter, this feature lies at the heart of a fundamental problem plaguing an attempt to provide a fully coherent quantum mechanical account of a measurement process.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Peres, Phys. Rev. D 22, 879 (1980).

    ADS  Google Scholar 

  2. P. Holland, Quantum Theory of Motion (Cambridge Univer. Press, Cambridge, 1993), pp. sect. 8.3.2.

    Google Scholar 

  3. J. von Neumann, Die Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin, 1932); English translation: Mathematical Foundations of Quantum Mechanics (Princeton Univer. Press, Princeton, NJ, 1955).

    Google Scholar 

  4. W. Lamb, in Noise and Chaos in Nonlinear Dynamical Systems (F. Moss et al, eds.) (Cambridge Univer. Press, Cambridge, 1990).

    Google Scholar 

  5. M. O. Scully, R. Shea, and J. D. McCullen, Phys. Rep. 43, 485 (1978).

    ADS  Google Scholar 

  6. M. Cini, Nuov. Cim. B 73, 27 (1983).

    MathSciNet  ADS  Google Scholar 

  7. M. Cini, in Quantum Theory without Reduction (M. Cini and J. M. Levy-Leblond, eds.) (Adam Hilger, Bristol, UK, 1990).

    Google Scholar 

  8. D. F. Walls, M. J. Collet, and G. J. Milburn, Phys. Rev. D 32, 3208 (1985).

    MathSciNet  ADS  Google Scholar 

  9. P. Busch, P. J. Lahti, and P. Mittelstaedt, Quantum Theory of Measurement (Springer-Verlag, Berlin, 1991).

    Google Scholar 

  10. Y. Aharonov and J. L. Safko, Ann. Phys. 91, 279 (1975).

    ADS  Google Scholar 

  11. K. Hepp, Helv. Phys. Acta 45, 237 (1972).

    Google Scholar 

  12. A. B. Pippard, Eur. J. Phys. 7, 43 (1986).

    MathSciNet  Google Scholar 

  13. P. W. Anderson, in Lesson of Quantum Theory (J. de Boer et al., eds.) (Elsevier, Amsterdam, 1986).

    Google Scholar 

  14. P. Alstrom, P. Hjorth, and R. Mattuck, Am. J. Phys. 50, 697 (1982).

    ADS  Google Scholar 

  15. M. O. Scully, W. E. Lamb, and A. Barut, Found. Phys. 17, 575 (1987).

    MathSciNet  ADS  Google Scholar 

  16. N. F. Mott, Proc. Roy Soc. A 126, 79 (1929).

    ADS  MATH  Google Scholar 

  17. J. S. Bell, in Speakable and Unspeakable in Quantum Mechanics (Cambridge Univer. Press, Cambridge, 1987), pp. 120–21.

    MATH  Google Scholar 

  18. E. P. Wigner, Annals of the New York Academy of Sciences 480, 5 (1986).

    MathSciNet  ADS  Google Scholar 

  19. W. V. Quine, in Problems in the Philosophy of Science (I. Lakatos and A. Musgrave, eds.) (North-Holland, Amsterdam, 1968), pp. 200–204.

    Google Scholar 

  20. S. Weinberg, Dreams of a Pinal Theory (Vintage, London, 1993), p. 64.

    Google Scholar 

  21. W. E. Lamb, in Ta-You Wu Festschrift: Science of Matter (S. Fujita, ed.) (Gordon and Breach, New York, 1979), pp. 7–8.

    Google Scholar 

  22. J. S. Bell, in Speakable and Unspeakable in Quantum Mechanics (Cambridge Univer. Press, Cambridge, 1987), p. 125.

    MATH  Google Scholar 

  23. E. P. Wigner, Am. J. Phys. 31, 6 (1963).

    MathSciNet  ADS  MATH  Google Scholar 

  24. A. J. Leggett, in Lesson of Quantum Theory (J. de Boer, E. Dal, and O. Ulfbeck, eds.) (Elsevier, Amsterdam, 1986), p. 47.

    Google Scholar 

  25. N. Bohr, Essays 1958/1962 on Atomic Physics and Human Knowledge (Wiley, New York, 1963), p. 3.

    MATH  Google Scholar 

  26. N. Bohr, Essays 1958/1962 on Atomic Physics and Human Knowledge (Wiley, New York, 1963), p. 60.

    MATH  Google Scholar 

  27. N. Bohr, Dialectica 2, 312 (1948).

    MATH  Google Scholar 

  28. W. Moore, Schrödinger—Life and Thought (Cambridge Univer. Press, Cambridge, 1989), pp. 312–313.

    Google Scholar 

  29. N. Bohr, Atomic Physics and Human Knowledge (Wiley, New York, 1958), pp. 32–66.

    MATH  Google Scholar 

  30. P. K. Feyerabend, in Frontiers of Science and Philosophy (R. G. Colodny, Ă©d.) (Univer. of Pittsburgh Press, Pittsburgh, 1962), p. 219.

    Google Scholar 

  31. M. Jammer, Philosophy of Quantum Mechanics (Wiley-Interscience, New York, 1974), p. 207.

    Google Scholar 

  32. W. Heisenberg, Physical Principles of the Quantum Theory (Univer. of Chicago Press, Chicago, 1930; reprinted Dover, New York), p. 64.

    MATH  Google Scholar 

  33. J. S. Bell, in Speakable and Unspeakable in Quantum Mechanics (Cambridge Univer. Press, Cambridge, 1987), p. 124.

    MATH  Google Scholar 

  34. L. Rosenfeld, Suppl. Prog. Theo. Phys. 222, 1 (1965).

    Google Scholar 

  35. W. Heisenberg, in Niels Bohr and the Development of Physics (W. Pauli, ed.) (Pergamon Press, Oxford, UK, 1955), pp. 12–29.

    Google Scholar 

  36. W. Heisenberg, Physics and Philosophy (Harper and Row, New York, 1962), chap. 3.

    Google Scholar 

  37. A. Peres and W. H. Zurek, Am. J. Phys. 50, 807 (1982).

    ADS  Google Scholar 

  38. A. Peres, Am. J. Phys. 54, 688 (1986).

    ADS  Google Scholar 

  39. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, Netherlands, 1993), chap. 12.

    MATH  Google Scholar 

  40. A. B. Pippard, Eur. J. Phys. 7, 43 (1986).

    MathSciNet  Google Scholar 

  41. A. Zeilinger, in Quantum Theory without Reduction (M. Cini and J. M. Levy-Leblond, eds.) (Adam Hilger, Bristol, UK, 1989), pp. 18.

    Google Scholar 

  42. R. Peierls, Phys. World, 4, 19 (Jan. 1991).

    Google Scholar 

  43. N. G. van Kampen, in Proc. 3d Int. Symp. Foundations of Quantum Mechanics (Physical Society of Japan, Tokyo, 1989), pp. 107–14.

    Google Scholar 

  44. L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970).

    ADS  MATH  Google Scholar 

  45. D. Home and M. A. B. Whitaker, Phys. Rep. 210, 223 (1992), sects. 5.4 and 6.2.

    MathSciNet  ADS  Google Scholar 

  46. W. H. Zurek, Prog. Theor. Phys. 89, 281 (1993).

    MathSciNet  ADS  Google Scholar 

  47. K. Gottfried, Phys. World 4, 10, 34 (1991).

    Google Scholar 

  48. A. J. Leggett, Contemp. Phys. 25, 583 (1984).

    ADS  Google Scholar 

  49. A. J. Leggett, in Quantum Implications (B. J. Hiley, F. D. Peat, eds.) (Routledge and Kegan Paul, London, 1987), pp. 85–104.

    Google Scholar 

  50. A. J. Leggett, in Proc. 1st Int. Symp. Foundations of Quantum Mechanics in the Light of New Technology (Physical Society of Japan, Tokyo, 1984).

    Google Scholar 

  51. A. J. Leggett, Prog. Theor. Phys. Suppl., no. 69, 80 (1980).

    Google Scholar 

  52. R. Omnés, Interpretation of Quantum Mechanics (Princeton Univer. Press, Princeton, NJ, 1994), chap. 7.

    MATH  Google Scholar 

  53. N. G. van Kampen, Physica A 153, 97 (1988).

    MathSciNet  ADS  Google Scholar 

  54. A. J. Leggett, Curr. Sci. 67, 785 (1994).

    Google Scholar 

  55. J. S. Bell, Phys. World 3, no. 8, 33 (1990).

    Google Scholar 

  56. J. S. Bell, also in: Sixty-Two Years of Uncertainty (A. I. Miller, ed.) (Plenum, New York, 1990), pp. 17–31.

    Google Scholar 

  57. B. d’Espagnat, Veiled Reality—an Analysis of Pre sent-Day Quantum Mechanical Concepts (Addison-Wesley, Reading, MA, 1995), chap. 10.

    Google Scholar 

  58. R. Omnés, Found. Phys. 25, 605 (1995).

    MathSciNet  ADS  Google Scholar 

  59. K. Gottfried, Quantum Mechanics (W. A. Benjamin, New York, 1966), chap. 4.

    Google Scholar 

  60. C. F von Weizsäcker and Th. Görnitz, Found. Phys. 21, 311 (1991).

    Google Scholar 

  61. R. B. Griffiths, J. Stat. Phys. 36, 219 (1984).

    ADS  MATH  Google Scholar 

  62. R. B. Griffiths, in New Techniques and Ideas in Quantum Measurement Theory (D. M. Greenberger, ed.) (New York Academy of Sciences, New York, 1986).

    Google Scholar 

  63. R. B. Griffiths, Found. Phys. 23, 1601 (1993).

    MathSciNet  ADS  Google Scholar 

  64. R. Omnés, J. Stat. Phys. 53, 893 (1988).

    ADS  MATH  Google Scholar 

  65. R. Omnés, Rev. Mod. Phys. 64, 339 (1992).

    ADS  Google Scholar 

  66. M. Gell-Mann and J. B. Hartle, in Complexity, Entropy, and the Physics of Information (W. Zurek, ed.) (Addison-Wesley, Reading, MA, 1990).

    Google Scholar 

  67. M. Gell-Mann and J. B. Hartle, in Proc. 3d Int. Symp. Foundations of Quantum Mechanics in the Light of New Technology (S. Kobayashi et al, eds.) (Phys. Soc. of Japan, Tokyo, 1990).

    Google Scholar 

  68. M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993).

    MathSciNet  ADS  Google Scholar 

  69. B. d’Espagnat, J. Stat. Phys. 56, 747 (1989).

    MathSciNet  ADS  Google Scholar 

  70. B. d’Espagnat, Found. Phys. 20, 1147 (1990).

    MathSciNet  ADS  Google Scholar 

  71. M. Gell-Mann, Quark and the Jaguar (Little Brown and Co., London, 1994), pp. 153–54.

    MATH  Google Scholar 

  72. P. A. M. Dirac, in Electrons et Photons—Rapports et Discussions du Cinquième Conseil de Physique tenu à Bruxelles 1927 (Gauthier-Villars, Paris, 1928).

    Google Scholar 

  73. P. A. M. Dirac, Principles of Quantum Mechanics (Clarendon, Oxford, UK, 1930), p. 36.

    MATH  Google Scholar 

  74. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, UK, 1977), p. 22.

    Google Scholar 

  75. L. E. Ballentine, Found. Phys. 20, 1329 (1990).

    MathSciNet  ADS  Google Scholar 

  76. L. E. Ballentine, Quantum Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1990), chap. 9.

    Google Scholar 

  77. L. D. Landau and R. Peierls, Z. Phys. 69, 56 (1931).

    ADS  Google Scholar 

  78. L. E. Ballentine, in Fundamental Questions in Quantum Mechanics (L. M. Roth and A. Inomata, eds.) (Gordon and Breach, New York, 1986), pp. 65–75.

    Google Scholar 

  79. H. Everett, Rev. Mod. Phys. 29, 454 (1957).

    MathSciNet  ADS  Google Scholar 

  80. E. J. Squires, in Quantum Theory without Reduction (M. Cini and J. M. Levy-Leblond, eds.) (Adam-Hilger, Bristol, UK, 1989).

    Google Scholar 

  81. E. J. Squires, Synthese 97, 109 (1993).

    MathSciNet  Google Scholar 

  82. B. S. Dewitt and N. Graham, Many-Worlds Interpretation of Quantum Mechanics (Princeton Univer. Press, Princeton, NJ, 1973), pp. 155–65.

    Google Scholar 

  83. L. E. Ballentine, Found. Phys. 3, 229 (1973).

    ADS  Google Scholar 

  84. D. Deutsch, Int. J. Theor. Phys. 24, 1 (1985).

    MathSciNet  Google Scholar 

  85. M. Lockwood, Mind, Brain, and the Quantum (Basil Blackwell, Oxford, UK, 1989), chap. 13.

    Google Scholar 

  86. D. Albert and B. Loewer, Synthese 77, 195 (1988).

    MathSciNet  Google Scholar 

  87. H. P. Stapp, Mind, Matter, and Quantum Mechanics (Springer-Verlag, Berlin, 1993).

    MATH  Google Scholar 

  88. H. Primas, Chemistry, Quantum Mechanics, and Reductionism (Springer-Verlag, Berlin, 1981), pp. sect. 3.6.

    Google Scholar 

  89. D. Bohm and B. J. Hiley, Undivided universe (Routledge, London, 1993), p. 311.

    Google Scholar 

  90. H. Everett, in Many-Worlds Interpretation of Quantum Mechanics (B. S. DeWitt and N. Graham, eds.) (Princeton Univer. Press, Princeton, NJ, 1973), pp. 100.

    Google Scholar 

  91. J. Schwinger, M. O. Scully, and B. G. Englert, Z. Phys. D 10, 135 (1988).

    ADS  Google Scholar 

  92. B. G. Englert, J. Schwinger, and M. O. Scully, Found. Phys. 18, 1045 (1988).

    MathSciNet  ADS  Google Scholar 

  93. B. d’Espagnat, Veiled Reality—an Analysis of Present-Day Quantum Mechanical Concepts (Addison-Wesley, Reading, MA, 1995), pp. 282–83.

    Google Scholar 

  94. N. Gisin, Phys. Lett. A 143, 1 (1990).

    ADS  Google Scholar 

  95. J. Polchinski, Phys. Rev. Lett. 66, 397 (1991).

    MathSciNet  ADS  MATH  Google Scholar 

  96. S. Weinberg, Dreams of a Final Theory (Vintage, London, 1993), pp. 69–70.

    Google Scholar 

  97. G. C. Ghirardi, A. Rimini, and T. Weber, in Quantum Probability and Applications (L. Accardi and W. von Waldenfels, eds.) (Springer-Verlag, Berlin, 1985), pp. 223–32.

    Google Scholar 

  98. G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986).

    MathSciNet  ADS  MATH  Google Scholar 

  99. E. J. Squires, Phys. Lett. A 158, 431 (1991).

    ADS  Google Scholar 

  100. P. Pearle and E. Squires, Phys. Rev. Lett. 73, 1 (1994).

    ADS  Google Scholar 

  101. D. Z. Albert and B. Loewer, in Perspectives on Quantum Reality (R. Clifton, ed.) (Kluwer, Dordrecht, Netherlands, 1996), pp. 81–92.

    Google Scholar 

  102. D. Z. Albert and B. Loewer, in Proc. Philosophy of Science Association, vol. 1 (A. Fine et al., eds.), pp. 277-85.

    Google Scholar 

  103. D. Z. Albert and L. Vaidman, Phys. Lett. A 139, 1 (1989). D. Z. Albert and L. Vaidman, 171, 438 (1992).

    MathSciNet  ADS  Google Scholar 

  104. F. Aicardi, A. Borsellino, G. C. Ghirardi, and R. Grassi, Found. Phys. Lett. 4, 109 (1991).

    Google Scholar 

  105. C. Dove and E. J. Squires, Symmetric Versions of Explicit Wave Function Collapse Models (Univer. of Durhan, Preprint DTP/94/45, 1994).

    Google Scholar 

  106. P. Pearle, Phys. Rev. A 39, 2277 (1989).

    ADS  Google Scholar 

  107. G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990).

    MathSciNet  ADS  Google Scholar 

  108. G. C. Ghirardi and A. Rimini, in Sixty-Two Years of Uncertainty (A. Miller, ed.) (Plenum, New York, 1990), pp. 167–91.

    Google Scholar 

  109. G. C. Ghirardi in Fundamental Problems in Quantum Theory (D. M. Greenberger and A. Zeilinger, eds.) (New York Academy of Sciences, New York, 1995).

    Google Scholar 

  110. G. C. Ghirardi, R. Grassi, and A. Rimini, Phys. Rev. A 42, 1057 (1990).

    ADS  Google Scholar 

  111. A. Rimini, in International Course on Advances on Quantum Phenomena (E. Beltrametti and J. M. Levy-Leblond, eds.) (Plenum, New York, 1994).

    Google Scholar 

  112. A. Shimony, in Proc. Philosophy of Science Association, vol. 2 (A. Fine et al., eds.).

    Google Scholar 

  113. G. C. Ghirardi, R. Grassi, and F. Benatti, Found. Phys. 25, 5 (1995).

    MathSciNet  ADS  MATH  Google Scholar 

  114. J. S. Bell, in Speakable and Unspeakable in Quantum Mechanics (Cambridge Univer. Press, Cambridge, 1987), p. 117.

    MATH  Google Scholar 

  115. G. C. Ghirardi and R. Grassi, in Bohmian Mechanics and Quantum Theory: An Appraisal (J. T. Cushing, A. Fine, and S. Goldstein, eds.) (Kluwer, Dordrecht, Netherlands, 1996), pp. 353–77.

    Google Scholar 

  116. D. Bohm and B. J. Hiley, Undivided Universe (Routledge, London, 1993), pp. 326–28.

    Google Scholar 

  117. P. Holland, Found. Phys., to be published.

    Google Scholar 

  118. S. Machida and M. Namiki, Prog Theor. Phys. 63, 1457, 1833 (1980).

    ADS  Google Scholar 

  119. M. Namiki, Ann. NY Acad. Sci. 480, 78 (1986).

    ADS  Google Scholar 

  120. M. Namiki, Found. Phys. 18, 29 (1988).

    MathSciNet  ADS  Google Scholar 

  121. M. Namiki and S. Pascazio, Phys. Rep. 232, 301 (1993).

    MathSciNet  ADS  Google Scholar 

  122. R. Penrose, Shadows of the Mind (Oxford Univer. Press, Oxford, UK, 1994), chap. 6.

    Google Scholar 

  123. I. Prigogine and C. George, Proc. Nat. Acad. Sci. (USA) 80, 4590 (1983).

    MathSciNet  ADS  MATH  Google Scholar 

  124. T. Petrosky and I. Prigogine, Liouville Space Extension of Quantum Mechanics, to appear in Adv. Chem. Phys. (1997).

    Google Scholar 

  125. B. Misra, I. Prigogine, and M. Courbage, Proc. Nat. Acad. Sci. (USA) 76, 4768 (1979).

    MathSciNet  ADS  Google Scholar 

  126. I. Prigogine and I. Stengers, Order out of Chaos (Bantam Books, New York, 1984).

    Google Scholar 

  127. D. Home and S. Bose, Phys. Lett. A (1996).

    Google Scholar 

  128. W. H. Zurek, in Conceptual Problems of Quantum Gravity (A. Ashtekar and J. Stachel, eds.) (Birhauser, Boston, 1991).

    Google Scholar 

  129. W. H. Zurek, Phys. Today 44, 36 (1991).

    Google Scholar 

  130. W. H. Zurek, Prog. Theor. Phys. 89, 281 (1993).

    MathSciNet  ADS  Google Scholar 

  131. D. M. Greenberger and A. Yasin, in Proc. 2d Int. Symp. Foundations of Quantum Mechanics (M. Namiki et al, eds.) (Phys. Soc. Japan, Tokyo, 1987), pp. 18–24.

    Google Scholar 

  132. D. Home and R. Chattopadhyaya, Phys. Rev. Lett. 76, 2836 (1996).

    MathSciNet  ADS  MATH  Google Scholar 

  133. A. Rae, Quantum Physics: Illusion or Reality? (Cambridge Univer. Press, Cambridge, 1986), p. 61.

    Google Scholar 

  134. A. Shimony, in Philosophical Consequences of Quantum Theory (J. T. Cushing and E. Mcmullin, eds.) (Univer. of Notre Dame Press, Notre Dame, IN, 1989), p. 36.

    Google Scholar 

  135. I. Percival, Nature 351, 357 (1991).

    ADS  Google Scholar 

  136. I. Husain and A. Sancar, Nucleic Acids Res. 15, 1109 (1987).

    Google Scholar 

  137. G. B. Sancar, F. W. Smith, R. Reid, G. Payne, M. Levy, and A. Sancar, J. Biol. Chem. 262, 478 (1987).

    Google Scholar 

  138. G. B. Sancar, F. W. Smith, and A. Sancar, Biochemistry 24, 1849 (1985).

    Google Scholar 

  139. N. Gisin and I. Percival, J. Phys. A 26, 2245 (1993).

    MathSciNet  ADS  Google Scholar 

  140. F. Aicardi, A. Borsellino, G. C. Ghirardi, and R. Grassi, Found. Phys. Lett. 4, 116 (1991).

    Google Scholar 

  141. A. Venugopalan, Phys. Rev. A 50, 2742 (1994).

    ADS  Google Scholar 

  142. I. Husain, J. Griffith, and A. Sancar, Proc. Nat. Acad. Sci (USA) 85, 2558 (1988).

    ADS  Google Scholar 

  143. J. S. Bell, in Ghost in the Atom (P. C. W. Davies and J. R. Brown, eds.) (Cambridge Univer. Press, Cambridge, 1986), p. 54.

    Google Scholar 

  144. A. J. Leggett, Curr. Sci. 67, 785 (1994).

    Google Scholar 

  145. R. P. Feynman, in Feynman Lectures on Gravitation (F. B. Morinigo, W. G. Wagner, and B. Hatfield, eds.), pp. 12 and 15, Addison-Wesley, Massachusetts (1995).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Home, D. (1997). Quantum Measurement Paradox. In: Conceptual Foundations of Quantum Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9808-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9808-1_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9810-4

  • Online ISBN: 978-1-4757-9808-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics