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Trudy Mat. Inst. Steklova, 2009, Volume 265, Pages 288–319 (Mi tm842)  

This article is cited in 4 scientific papers (total in 4 papers)

Squeezed Quantum States on an Interval and Uncertainty Relations for Nanoscale Systems

I. V. Volovich, A. S. Trushechkin

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: We construct families of squeezed quantum states on an interval and analyze their asymptotic behavior. We study the localization properties of a kind of such states constructed on the basis of the theta function. For the coordinate and momentum dispersions of a quantum particle on an interval, we obtain estimates that apply, in particular, to nanoscale systems.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 265, 276–306

Bibliographic databases:

UDC: 517.958:530.145
Received in December 2008

Citation: I. V. Volovich, A. S. Trushechkin, “Squeezed Quantum States on an Interval and Uncertainty Relations for Nanoscale Systems”, Selected topics of mathematical physics and $p$-adic analysis, Collected papers, Trudy Mat. Inst. Steklova, 265, MAIK Nauka/Interperiodica, Moscow, 2009, 288–319; Proc. Steklov Inst. Math., 265 (2009), 276–306

Citation in format AMSBIB
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\by I.~V.~Volovich, A.~S.~Trushechkin
\paper Squeezed Quantum States on an Interval and Uncertainty Relations for Nanoscale Systems
\inbook Selected topics of mathematical physics and $p$-adic analysis
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2009
\vol 265
\pages 288--319
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm842}
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\jour Proc. Steklov Inst. Math.
\yr 2009
\vol 265
\pages 276--306
\crossref{https://doi.org/10.1134/S0081543809020254}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Volovich I.V., “Randomness in classical mechanics and quantum mechanics”, Found. Phys., 41:3 (2011), 516–528  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. I. V. Volovich, A. S. Trushechkin, “Asymptotic properties of quantum dynamics in bounded domains at various time scales”, Izv. Math., 76:1 (2012), 39–78  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Furuichi Sh., Yanagi K., “Schrödinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure”, J. Math. Anal. Appl., 388:2 (2012), 1147–1156  crossref  mathscinet  zmath  isi  elib  scopus
    4. Trushechkin A., “Semiclassical Evolution of Quantum Wave Packets on the Torus Beyond the Ehrenfest Time in Terms of Husimi Distributions”, J. Math. Phys., 58:6 (2017), 062102  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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