Communications in Mathematical Physics

, Volume 9, Issue 4, pp 303–312 | Cite as

On the derivation of the Schroedinger equation in a Riemannian manifold

  • K. R. Parthasarathy


Under certain conditions it is shown that the kinetic part of the dynamical operator of a quantum mechanical system with a Riemannian manifold as configuration space is the Laplace-Beltrami operator.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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  1. 1.
    Eisenhart, L. P.: Riemannian geometry. Princeton: University Press 1949.Google Scholar
  2. 2.
    Mackey, G. W.: The mathematical foundations of quantum mechanics. New York: Benjamin 1963.Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • K. R. Parthasarathy
    • 1
  1. 1.Statistical LaboratoryUniversity of ManchesterManchester 13Great Britain

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