Advertisement

Foundations of Physics

, Volume 10, Issue 3–4, pp 217–236 | Cite as

A modified set of Feynman postulates in quantum mechanics

  • V. K. Thankappan
  • P. Gopalakrishna Nambi
Article

Abstract

Certain modifications, by way of improvement, are proposed for the Feynman postulates in quantum mechanics. These modifications incorporate a criterion for the applicability of the principle of superposition. It is shown that the modified postulates, together with certain assumptions regarding the trajectory of a particle, lead to an expression for the position-momentum uncertainty relationship which is broadly in agreement with the conventional expression. The time-energy uncertainty relationship is, however, found to have a likely place only in the relativistic theory. A criterion, in the form of a ratio involving the linear dimensions of the particle, is obtained for the validity of the classical mechanics approximation. The modified postulates are suggested to favor the statistical interpretation of quantum mechanics over the Copenhagen interpretation.

Keywords

Quantum Mechanic Classical Mechanic Linear Dimension Relativistic Theory Statistical Interpretation 
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. P. Feynman,Rev. Mod. Phys. 20, 367 (1948).Google Scholar
  2. 2.
    R. P. Feynman and A. R. Hibbs,Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).Google Scholar
  3. 3.
    D. ter Haar,Elements of Statistical Mechanics (Holt, Rinehart and Winston, New York, 1961), p. 101.Google Scholar
  4. 4.
    H. Goldstein,Classical Mechanics (Addison-Wesley, Reading, Mass., 1959), Section 7–5.Google Scholar
  5. 5.
    L. D. Landau and E. M. Lifshitz,Mechanics, 2nd ed. (Pergamon Press, Oxford, 1969), Section 4.3.Google Scholar
  6. 6.
    H. Margenau and L. Cohen, Probabilities in Quantum Mechanics, inQuantum Theory and Reality, M. Bunge, ed. (Springer-Verlag, Berlin, 1967), Chapter 4.Google Scholar
  7. 7.
    E. Merzbacher,Quantum Mechanics, 2nd ed. (Wiley, New York, 1970), pp. 158–161.Google Scholar
  8. 8.
    A. Landé,Am. J. Phys. 43, 701 (1975).Google Scholar
  9. 9.
    L. D. Landau and E. M. Lifshitz,Statistical Physics (Pergamon Press, Oxford, 1969), p. 1.Google Scholar
  10. 10.
    L. E. Ballentine,Rev. Mod. Phys. 42, 358 (1970).Google Scholar
  11. 11.
    M. Jammer,Conceptual Development of Quantum Mechanics (McGraw-Hill, New York 1966), Chapter 7; see also H. P. Stapp,Am. J. Phys. 40, 1098 (1972).Google Scholar
  12. 12.
    R. D. Prosser,Int. J. Theor. Phys. 15, 181 (1976).Google Scholar
  13. 13.
    M. Bunge,Can. J. Phys. 48, 1410 (1970).Google Scholar
  14. 14.
    G. R. Allcock,Ann. Phys. 53, 311 (1969), Section VII.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • V. K. Thankappan
    • 1
  • P. Gopalakrishna Nambi
    • 2
  1. 1.Physics DepartmentUniversity of CalicutKeralaIndia
  2. 2.Physics DepartmentMalabar Christian CollegeCalicutIndia

Personalised recommendations