Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




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

Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 154, Number 2, Pages 363–371
DOI: https://doi.org/10.4213/tmf6175 (Mi tmf6175) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice

M. I. Muminov

A. Navoi Samarkand State University
Full-text PDF (376 kB) Citations (2)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf6175
Abstract: We consider a system of three quantum particles interacting by pairwise short-range attraction potentials on a three-dimensional lattice (one of the particles has an infinite mass). We prove that the number of bound states of the corresponding Schrödinger operator is finite in the case where the potentials satisfy certain conditions, the two two-particle sub-Hamiltonians with infinite mass have a resonance at zero, and zero is a regular point for the two-particle sub-Hamiltonian with finite mass.
Keywords: resonance, two-particle sub-Hamiltonian, discrete spectrum, variation principle.
Received: 21.02.2007
English version:
Theoretical and Mathematical Physics, 2008, Volume 154, Issue 2, Pages 311–318
DOI: https://doi.org/10.1007/s11232-008-0029-4
Bibliographic databases:
Language: Russian
Citation: M. I. Muminov, “Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice”, TMF, 154:2 (2008), 363–371; Theoret. and Math. Phys., 154:2 (2008), 311–318
Citation in format AMSBIB
\Bibitem{Mum08}
\by M.~I.~Muminov
\paper Finiteness of the~discrete spectrum of the~Schr\"odinger operator of
three particles on a~lattice
\jour TMF
\yr 2008
\vol 154
\issue 2
\pages 363--371
\mathnet{http://mi.mathnet.ru/tmf6175}
\crossref{https://doi.org/10.4213/tmf6175}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2424014}
\zmath{https://zbmath.org/?q=an:1150.81005}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2008TMP...154..311M}
\elib{https://elibrary.ru/item.asp?id=10438480}
\transl
\jour Theoret. and Math. Phys.
\yr 2008
\vol 154
\issue 2
\pages 311--318
\crossref{https://doi.org/10.1007/s11232-008-0029-4}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000253216500013}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-39349110537}
Linking options:
  • https://www.mathnet.ru/eng/tmf6175
  • https://doi.org/10.4213/tmf6175
  • https://www.mathnet.ru/eng/tmf/v154/i2/p363
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:466
    Full-text PDF :213
    References:95
    First page:2
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024