Advertisement

Foundations of Physics

, Volume 10, Issue 1–2, pp 33–56 | Cite as

Quantum mechanics based on position

  • Ralph H. Young
This Issue Is Dedicated To The Memory Of Wolfgang Yourgrau

Abstract

The only observational quantity which quantum mechanics needs to address islocation. The typical primitive observation on a microsystem (e.g., photon) isdetection at alocation (e.g., by a photomultiplier “looking at” a grating). To analyze an experiment, (a) form a conceptual ensemble of replicas of it, (b) assign a wave function (in “position representation”) to its initial condition, (c) evolve the wave function by the Schrödinger equation (known, once and for all, as a function of the system's composition), (d) compute the probability for particle detection at various times and places. The initial wave function is chosen on the basis of experience with such treatments. Key experiments are thus treated: (i) time-of-flight, (ii) Stern-Gerlach, (iii) Franck-Hertz, (iv) photon recoil, (v) photoionization. Quantum states, dynamical variables, and measurements, and the usual postulates about them, are superfluous. The explicit treatments are nonrelativistic; the existence of relativistic generalizations is left open.

Keywords

Wave Function Quantum Mechanic Quantum State Dynamical Variable Initial Wave 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. H. Young, unpublished.Google Scholar
  2. 2.
    E. H. Kennard,Phys. Rev. 31, 876 (1928).Google Scholar
  3. 3.
    E. H. Kennard,J. Franklin Inst. 207, 495 (1929).Google Scholar
  4. 4.
    E. C. Kemble,The Fundamental Principles of Quantum Mechanics (Dover, New York, 1958), esp. Sections 14a, b; 15; 33b; 41.Google Scholar
  5. 5.
    W. Pauli, Die allgemeinen Prinzipien der Wellenmechanik, inGeiger-Scheel Handbuch der Physik, Vol. 24, Part 1 (Springer, Berlin, 1933), Part A, p. 94 and Sections 9, 11.Google Scholar
  6. 6.
    R. P. Feynman and A. R. Hibbs,Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965), pp. 96–100.Google Scholar
  7. 7.
    N. Maxwell,Found. Phys. 6, 275, 661 (1976).Google Scholar
  8. 8.
    M. Bunge,Foundations of Physics (Springer, New York, 1967).Google Scholar
  9. 9.
    J. C. Slater,J. Franklin Inst. 207, 449 (1929).Google Scholar
  10. 10.
    J. Frenkel,Einführung in die Wellenmechanik (Springer, Berlin, 1929).Google Scholar
  11. 11.
    E. C. Kemble and E. L. Hill,Rev. Mod. Phys. 2, 1 (1930).Google Scholar
  12. 12.
    A. Einstein,J. Franklin Inst. 221, 349 (1936).Google Scholar
  13. 13.
    G. Temple,Rep. Prog. Phys. 1, 1 (1934).Google Scholar
  14. 14.
    A. Einstein, inAlbert Einstein: Philosopher-Scientist, P. A. Schlipp, ed. (Library of Living Philosophers, Evanston, Ill., 1949), pp. 665ff.Google Scholar
  15. 15.
    H. Margenau,Phil. Sci. 30, 1, 138 (1963).Google Scholar
  16. 16.
    D. I. Blokhintsev,Quantum Mechanics (Reidel, Dordrecht, 1964), Sections 14, 110, 111.Google Scholar
  17. 17.
    K. R. Popper, inQuantum Theory and Reality, M. Bunge, ed. (Springer, New York, 1967), pp. 7ff.Google Scholar
  18. 18.
    P. Pearle,Am. J. Phys. 35, 742 (1967).Google Scholar
  19. 19.
    J. L. Park,Am. J. Phys. 36, 211 (1968).Google Scholar
  20. 20.
    J. L. Park and H. Margenau,Int. J. Theor. Phys. 1, 211 (1968).Google Scholar
  21. 21.
    L. E. Ballentine,Rev. Mod. Phys. 42, 358 (1970).Google Scholar
  22. 22.
    H. J. Groenewold, inInduction, Physics, and Ethics, P. Weingartner and G. Zecha, eds. (Reidel, Dordrecht, 1970), p. 180ff.Google Scholar
  23. 23.
    B. D'Espagnat,Conceptual Foundations of Quantum Mechanics (Benjamin, Menlo Park, Calif., 1971).Google Scholar
  24. 24.
    F. J. Belinfante,Measurements and Time Reversal in Objective Quantum Theory (Pergamon, New York, 1975).Google Scholar
  25. 25.
    A. A. Ross-Bonney,Nuovo Cim. 30 B, 55 (1975).Google Scholar
  26. 26.
    J. L. Park and W. Band,Found. Phys. 6, 157 (1976).Google Scholar
  27. 27.
    L. S. Mayants, W. Yourgrau, and A. J. van der Merwe,Ann. Physik 33, 21 (1976).Google Scholar
  28. 28.
    U. Fano,Rev. Mod. Phys. 29, 74 (1957).Google Scholar
  29. 29.
    D. L. Reisler,Am. J. Phys. 39, 821 (1971).Google Scholar
  30. 30.
    W. Pauli, Ref. 5, Eq. (326), p. 189.Google Scholar
  31. 31.
    N. F. Mott and I. W. Sneddon,Wave Mechanics and Its Applications (Oxford, 1948), Sections 13, 14, 27.Google Scholar
  32. 32.
    N. F. Mott and H. S. W. Massey,The Theory of Atomic Collisions, 3rd ed. (Oxford, New York, 1965), Chapter XI, Section 4.Google Scholar
  33. 33.
    R. P. Feynman, R. B. Leighton, and M. Sands,The Feynman Lectures on Physics (Addison-Wesley, New York, 1964), Vol. III, Section 11-1.Google Scholar
  34. 34.
    A. Messiah,Quantum Mechanics (North-Holland, Amsterdam, 1961), Chapter II, Sections 3, 15; Chapter IV, Section 14; Chapter V, Section 13; Chapter X, Sections 6, 16.Google Scholar
  35. 35.
    H. A. Kramers,Quantum Mechanics (Dover, New York, 1964), Sections 11, 15, 60.Google Scholar
  36. 36.
    L. I. Schiff,Quantum Mechanics, 3rd ed. (McGraw-Hill, New York, 1968), Sections 35, 49 and Chapter 11.Google Scholar
  37. 37.
    M. Born and R. Oppenheimer,Ann. Physik 84, 457 (1927).Google Scholar
  38. 38.
    P. A. M. Dirac,Proc. Roy. Soc. Lond. 114 A, 243 (1927).Google Scholar
  39. 39.
    W. Raith,Adv. Atomic Molec. Phys. 12, 281 (1976).Google Scholar
  40. 40.
    W. Heisenberg,The Physical Principles of the Quantum Theory (Dover, New York, 1949), Chapter II, Section 2.Google Scholar
  41. 41.
    C. G. Darwin,Proc. Roy. Soc. Lond. 117, 258 (1927).Google Scholar
  42. 42.
    L. De Broglie,An Introduction to the Study of Wave Mechanics (Methuen, London, 1930), pp. 156–168.Google Scholar
  43. 43.
    M. Reed and B. Simon,Methods of Mathematical Physics (Academic, New York, 1975), Vol. II, Section IX.7.Google Scholar
  44. 44.
    H. M. Nussenzveig,Causality and Dispersion Relations (Academic, New York, 1972), pp. 402–403.Google Scholar
  45. 45.
    D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, N. J., 1951), Sections 5.9, 20.3; Chapter 22.Google Scholar
  46. 46.
    F. London and E. Bauer,La Théorie de l'Observation en Mécanique Quantique (Hermann, Paris, 1939), Section 12.Google Scholar
  47. 47.
    K. Gottfried,Quantum Mechanics (Benjamin, New York, 1966), Vol. 1, Chapter IV, and Section 16.Google Scholar
  48. 48.
    H. Hönl and C. Eckart,Phys. Z. 31, 145 (1930).Google Scholar
  49. 49.
    N. Ramsey,Molecular Beams (Oxford, 1956), Sections I.2, XIV.3.Google Scholar
  50. 50.
    J. E. Sherwood, T. S. Stephenson, and S. Bernstein,Phys. Rev. 96, 1546 (1954).Google Scholar
  51. 51.
    H. G. Hasler and G. Weber,Atomkernenergie 7, 170 (1962).Google Scholar
  52. 52.
    R. H. Young,Am. J. Phys. 44, 581 (1976).Google Scholar
  53. 53.
    H. Margenau,Phil. Sci. 4, 337 (1937).Google Scholar
  54. 54.
    H. Margenau,The Nature of Physical Reality (McGraw-Hill, New York, 1950), Sections 18.4, 18.6.Google Scholar
  55. 55.
    H. Margenau,Phil. Sci. 25, 23 (1958).Google Scholar
  56. 56.
    H. Margenau,Phys. Rev. 49, 240 (1936).Google Scholar
  57. 57.
    H. Margenau,Ann. Phys. (N.Y.)23, 469 (1963).Google Scholar
  58. 58.
    J. L. Park,Phil. Sci. 35, 205, 389 (1968).Google Scholar
  59. 59.
    W. Band and J. L. Park,Found. Phys. 1, 133 (1970), Section 1.Google Scholar
  60. 60.
    D. J. Burns and W. H. Hancock,J. Opt. Soc. Am. 63, 241 (1973).Google Scholar
  61. 61.
    H. Walther, inLaser Spectroscopy of Atoms and Molecules, H. Walther, ed. (Springer, New York, 1976), pp. 88–93.Google Scholar
  62. 62.
    I. E. McCarthy and E. Weigold,Phys. Rep. 27 C, 275 (1976);Endeavour 2, 72 (1978).Google Scholar
  63. 63.
    L. D. Landau and E. M. Lifshitz,Quantum Mechanics, 2nd ed. (Pergamon, London, 1958), Section 44.Google Scholar
  64. 64.
    C. G. Darwin,Proc. Roy. Soc. Lond. 124 A, 375 (1929).Google Scholar
  65. 65.
    L. Eisenbud, Ph.D. Thesis, Princeton (1948).Google Scholar
  66. 66.
    F. Low, Lecture Notes (1953), unpublished (cited in Ref. 67).Google Scholar
  67. 67.
    M. L. Goldberger and K. M. Watson,Collision Theory (Wiley, New York, 1964) Chapters 3, 4.Google Scholar
  68. 68.
    J. R. Taylor,Scattering Theory (Wiley, New York, 1972), particularly Chapters 16, 17, 22 and Sections 3-d, 13-d, 20-e.Google Scholar
  69. 69.
    W. E. Lamb and R. C. Retherford,Phys. Rev. 79, 549 (1950).Google Scholar
  70. 70.
    H. S. W. Massey, E. H. S. Burhop, and H. B. Gilbody,Electronic and Ionic Impact Phenomena (Oxford, 1969), Sections 2.1.2.1, 2.1.3.Google Scholar
  71. 71.
    P. Jordan,Anschauliche Quantentheorie (Springer, Berlin, 1936), Chapter 1, Section 4, Part 2.Google Scholar
  72. 72.
    O. K. Rice,Phys. Rev. 35, 1538, 1551 (1930).Google Scholar
  73. 73.
    C. Lanczos,Z. Physik 68, 204 (1931).Google Scholar
  74. 74.
    A. M. Lane and R. G. Thomas,Rev. Mod. Phys. 30, 257 (1958), SectionXIII.4(b).Google Scholar
  75. 75.
    E. Merzbacher,Quantum Mechanics (Wiley, New York, 1961), pp. 126–130, 239–240.Google Scholar
  76. 76.
    L. R. Dodd and I. E. McCarthy,Phys. Rev. 134 A, 1136 (1964).Google Scholar
  77. 77.
    A. I. Baz', Ya. B. Zel'dovich, and A. M. Perelomov,Scattering, Reactions, and Decay in Nonrelativistic Quantum Mechanics (Israel Program for Scientific Translations, Jerusalem, 1969), Sections 29, 30, and references therein.Google Scholar
  78. 78.
    Ya. S. Grinberg,Izv. Vyssh. Ucheb. Zaved., Fiz., No. 12, p. 38 (1972).Google Scholar
  79. 79.
    H. Laue,Found. Phys. 8, 1 (1978).Google Scholar
  80. 80.
    O. Frisch,Z. Physik 86, 42 (1933).Google Scholar
  81. 81.
    R. Schneider, H. Walther, and L. Wöste,Opt. Comm. 5, 337 (1972).Google Scholar
  82. 82.
    J.-L. Picqué and J.-L. Vialle,Opt. Comm. 5, 402 (1972).Google Scholar
  83. 83.
    J. H. Shirley and S. Stenholm,J. Phys. A 10, 613 (1977).Google Scholar
  84. 84.
    S. R. Barone, M. A. Narcowich, and F. J. Narcowich,Phys. Rev. A 15, 1109 (1977).Google Scholar
  85. 85.
    A. P. Kazantsev,Usp. Fiz. Nauk 124, 113 (1978) [Sov. Phys.—Usp.21, 58 (1978)]; R. J. Cook,Phys. Rev. Lett. 41, 1788 (1978); R. J. Cook and A. F. Bernhardt,Phys. Rev. A 18, 2533 (1978).Google Scholar
  86. 86.
    H. A. Bethe,Ann. Physik 4, 443 (1930).Google Scholar
  87. 87.
    A. Sommerfeld,Atombau und Spektrallinien (Vieweg, Braunschweig, 1939), Vol. 2, Chapter 6, Section 7.Google Scholar
  88. 88.
    M. Von Laue, Korpuskular- und Wellentheorie, inMarx Handbuch der Radiologie, 2nd ed. (Akademische Verlagsgesellschaft, Leipzig, 1933), Vol.VI, Part 1, Section 7b.Google Scholar
  89. 89.
    J. D. Dollard,J. Math. Phys. 18, 229 (1977).Google Scholar
  90. 90.
    A. Asplund and L. Bungart,A First Course in Integration (Holt, Rinehart, and Winston, New York, 1966), p. 425.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Ralph H. Young
    • 1
  1. 1.Research LaboratoriesEastman Kodak CompanyRochester

Personalised recommendations