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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
Article

Abstract

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.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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.

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References

  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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