General Relativity and Gravitation

, Volume 8, Issue 2, pp 115–127 | Cite as

Remarks concerning the solution of the equations of quantum geometrodynamics by successive approximations

  • D. Christodoulou
  • M. Francaviglia
Research Articles


The improved version of the Einstein-Schrödinger equation of quantum gravity found by one of us is solved in the linear approximation. The solution differs from that obtained by K. Kuchař for the original version of the equation by an additional quantum effect: The energy, as deduced from measurements of the gravitational potential at infinity, has an error function probability distribution about its eigenvalue. The higher approximations are also considered and the appearance of a third quantum number, possibly related to the transition matrix, is deduced.


Probability Distribution Quantum Number Linear Approximation Quantum Gravity Function Probability 
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Copyright information

© Plenum Publishing Corp. 1977

Authors and Affiliations

  • D. Christodoulou
    • 1
  • M. Francaviglia
    • 2
  1. 1.International Centre for Theoretical PhysicsTrieste
  2. 2.Istituto di Fisica MatematicaUniversità di TorinoItaly

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