Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 1 scientific paper (total in 1 paper)

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

Full text: PDF file (218 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.5
Received in February 2014

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, Trudy Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 154–165; Proc. Steklov Inst. Math., 285 (2014), 145–156

Citation in format AMSBIB
\Bibitem{Iva14}
\by M.~G.~Ivanov
\paper Formulation of quantum mechanics with dynamical time
\inbook Selected topics of mathematical physics and analysis
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 285
\pages 154--165
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3540}
\crossref{https://doi.org/10.1134/S0371968514020113}
\elib{https://elibrary.ru/item.asp?id=21726847}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2014
\vol 285
\pages 145--156
\crossref{https://doi.org/10.1134/S0081543814040117}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000339949700011}
\elib{https://elibrary.ru/item.asp?id=24049968}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84926394011}


Linking options:
  • http://mi.mathnet.ru/eng/tm3540
  • https://doi.org/10.1134/S0371968514020113
  • http://mi.mathnet.ru/eng/tm/v285/p154

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:270
    Full text:219
    References:47

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021