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On the derivation of the Schroedinger equation in a Riemannian manifold

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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.

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References

  1. Eisenhart, L. P.: Riemannian geometry. Princeton: University Press 1949.

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  2. Mackey, G. W.: The mathematical foundations of quantum mechanics. New York: Benjamin 1963.

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Authors and Affiliations

  1. Statistical Laboratory, University of Manchester, Oxford Road, Manchester 13, Great Britain

    K. R. Parthasarathy

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  1. K. R. Parthasarathy
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Parthasarathy, K.R. On the derivation of the Schroedinger equation in a Riemannian manifold. Commun.Math. Phys. 9, 303–312 (1968). https://doi.org/10.1007/BF01654284

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  • DOI: https://doi.org/10.1007/BF01654284

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