Abstract
Quasiclassical representations are given for the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold. These give an unambiguous functional integral expression for the solution of the diffusion (heat) equation and a (formal) unambiguous functional integral expression for the wave function solution of the Schrödinger equation intimately related to a corresponding classical mechanical problem on the manifold. Guided by these expressions we prove that in the curved space background of a Riemannian manifold quantum mechanics tends to classical mechanics as ħ tends to zero.
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References
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© 1980 Plenum Press, New York
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Elworthy, D., Truman, A. (1980). The Classical Limit of Quantum Mechanics in a Curved Space Background. In: Antoine, JP., Tirapegui, E. (eds) Functional Integration. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-7035-6_5
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DOI: https://doi.org/10.1007/978-1-4615-7035-6_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4615-7037-0
Online ISBN: 978-1-4615-7035-6
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