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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Recursivity in quantum mechanics

Author: John C. Baez
Journal: Trans. Amer. Math. Soc. 280 (1983), 339-350
MSC: Primary 81B99; Secondary 03D80, 03E15, 81C10
MathSciNet review: 712264
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Abstract: The techniques of effective descriptive set theory are applied to the mathematical formalism of quantum mechanics in order to see whether it actually provides effective algorithms for the computation of various physically significant quantities, e.g. matrix elements. Various Hamiltonians are proven to be recursive (effectively computable) and shown to generate unitary groups which act recursively on the Hilbert space of physical states. In particular, it is shown that the $ n$-particle Coulombic Hamiltonian is recursive, and that the time evolution of $ n$-particle quantum Coulombic systems is recursive.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1983 American Mathematical Society