, Volume 10, Issue 3, pp 227–238 | Cite as

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

  • N Mukunda
  • E C G Sudarshan


In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.


Optical equivalence theorem coherent states overcomplete family of states discrete diagonal representation 


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  1. Agarwal G S and Wolf E 1970Phys. Rev. D2 2161ADSMathSciNetGoogle Scholar
  2. Bargmann V 1961Commun. Pure Appl. Math. 14 187MATHCrossRefMathSciNetGoogle Scholar
  3. Kano Y 1965J. Math. Phys. 6 1913CrossRefADSMathSciNetGoogle Scholar
  4. Klauder J R 1960Ann. Phys. (N. Y) 11 123MATHCrossRefADSMathSciNetGoogle Scholar
  5. Klauder J R, McKenna J and Currie D G 1965J. Math. Phys. 6 733ADSMathSciNetGoogle Scholar
  6. Klauder J R 1966Phys. Rev. Lett. 16 534CrossRefADSMathSciNetGoogle Scholar
  7. Klauder J R and Sudarshan E C G 1968Fundamentals of Quantum Optics (New York: W A Benjamin), Ch. 8Google Scholar
  8. Levinson N 1940Gap and Density Theorems AMS Colloquium Pub. Vol. 26, Ch. IVGoogle Scholar
  9. Mehta C L and Sudarshan E C G 1965Phys. Rev. 138B 274CrossRefADSMathSciNetGoogle Scholar
  10. Mehta C L 1967Phys. Rev. Lett. 18 752CrossRefADSGoogle Scholar
  11. Paley R E A C and Wiener N 1934Fourier Transforms in the Complex Domain AMS Colloquium Publications Vol. 19, Ch. VI, VIIGoogle Scholar
  12. Pool J C T 1966J. Math. Phys. 7 66MATHCrossRefADSMathSciNetGoogle Scholar
  13. Rocca F 1966Compt. Rend. 262 A547Google Scholar
  14. Sudarshan E C G 1963Phys. Rev. Lett. 10 277MATHCrossRefADSMathSciNetGoogle Scholar
  15. Sudarshan E C G 1969J. Math. Phys. Sci. 3 121MathSciNetGoogle Scholar
  16. Weyl H 1931The Theory of Groups and Quantum Mechanics (New York: Dover), p. 274MATHGoogle Scholar

Copyright information

© the Indian Academy of Sciences 1977

Authors and Affiliations

  • N Mukunda
    • 1
  • E C G Sudarshan
    • 1
  1. 1.Centre for Theoretical StudiesIndian Institute of ScienceBangalore
  2. 2.Department of PhysicsUniversity of TexasAustinUSA

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