, Volume 4, Issue 1, pp 1–18 | Cite as

The Hamilton-Jacobi equation revisited

  • K Babu Joseph
  • N Mukunda


A new analysis of the nature of the solutions of the Hamilton-Jacobi equation of classical dynamics is presented based on Caratheodory’s theorem concerning canonical transformations. The special role of a principal set of solutions is stressed, and the existence of analogous results in quantum mechanics is outlined.


Mechanics, classical Hamilton-Jacobi theory 


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  1. Caratheodory C 1965Calculus of variations and partial differential equations of the first order: Part I (Holden Day, Inc., San Francisco, California) Chapters 3 and 6.MATHGoogle Scholar
  2. Dirac P A M 1945Rev. Mod. Phys. 17 195MATHCrossRefADSMathSciNetGoogle Scholar
  3. Dirac P A M 1950Can. J. Math. 2 129MATHMathSciNetGoogle Scholar
  4. Dirac P A M 1951Can. J. Math. 3 1MATHMathSciNetGoogle Scholar
  5. Dirac P A M 1958The principles of quantum mechanics (The Clarendon Press, Oxford) 4th edition, Chapter V, Section 32MATHGoogle Scholar
  6. Goldstein H 1950Classical mechanics (Addison-Wesley Publishing Co., Inc., Reading, Mass.) Chapter 9Google Scholar
  7. Messiah A 1970Quantum mechanics I (North-Holland Publishing Company, Amsterdam) Chapter VIGoogle Scholar
  8. Mukunda N 1974Pramāna 2 1ADSGoogle Scholar
  9. Sudarshan E C G and Mukunda N 1974Classical dynamics: A modern perspective (Wiley-Interscience Publishers, New York) Chapter 6MATHGoogle Scholar
  10. Whittaker E T 1927A treatise on the analytical dynamics of particles and rigid bodies (Cambridge University Press) 3rd edition; Chapter IX, Section 126; Chapter XI, Sections 142, 143Google Scholar

Copyright information

© the Indian Academy of Sciences 1975

Authors and Affiliations

  • K Babu Joseph
    • 1
  • N Mukunda
    • 1
  1. 1.Centre for Theoretical StudiesIndian Institute of ScienceBangalore

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