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 Tr. Mat. Inst. Steklova, 2014, Volume 285, Pages 154–165 (Mi tm3540)

Formulation of quantum mechanics with dynamical time

M. G. Ivanov

Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Russia

Abstract: We consider quantum mechanics for which the system time is one of generalized coordinates. The generalized Hamiltonian has an unbounded spectrum, which allows us to introduce a Hermitian time operator. In the proposed formulation of quantum mechanics, a system time and observer's time are introduced. The Schrödinger equation in the system time either does not hold or holds only approximately. The wave function is assumed to be square integrable with respect to all coordinates, including the system time. In some limit, this formalism reproduces standard quantum mechanics and the corresponding measurement theory.

DOI: https://doi.org/10.1134/S0371968514020113

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 285, 145–156

Bibliographic databases:

Document Type: Article
UDC: 517.5

Citation: M. G. Ivanov, “Formulation of quantum mechanics with dynamical time”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Tr. Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 154–165; Proc. Steklov Inst. Math., 285 (2014), 145–156

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3540
• https://doi.org/10.1134/S0371968514020113
• http://mi.mathnet.ru/eng/tm/v285/p154

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This publication is cited in the following articles:
1. M. G. Ivanov, “Binary representation of coordinate and momentum in quantum mechanics”, Theoret. and Math. Phys., 196:1 (2018), 1002–1017
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