Abstract:
For the energy operator of a system of three one-dimensional or two-dimeasional
quantum particles conditions are found under which the discrete spectrum is finite
in spaces of functions of given symmetry. It follows from the obtained results in
particular that the Efimov effect is absent for the considered systems.
Citation:
S. A. Vugal'ter, G. M. Zhislin, “On the discrete spectrum of the energy operator of one- and two-dimensional quantum three-particle systems”, TMF, 55:2 (1983), 269–281; Theoret. and Math. Phys., 55:2 (1983), 493–502
\Bibitem{VugZhi83}
\by S.~A.~Vugal'ter, G.~M.~Zhislin
\paper On the discrete spectrum of the energy operator of one- and two-dimensional quantum three-particle systems
\jour TMF
\yr 1983
\vol 55
\issue 2
\pages 269--281
\mathnet{http://mi.mathnet.ru/tmf2167}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=734880}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 55
\issue 2
\pages 493--502
\crossref{https://doi.org/10.1007/BF01015810}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1983RV06700011}
Linking options:
https://www.mathnet.ru/eng/tmf2167
https://www.mathnet.ru/eng/tmf/v55/i2/p269
This publication is cited in the following 6 articles:
Simon Barth, Andreas Bitter, Semjon Vugalter, “The absence of the Efimov effect in systems of one- and two-dimensional particles”, Journal of Mathematical Physics, 62:12 (2021)
Lucas Happ, Matthias Zimmermann, Santiago I. Betelu, Wolfgang P. Schleich, Maxim A. Efremov, “Universality in a one-dimensional three-body system”, Phys. Rev. A, 100:1 (2019)
A G Volosniev, D V Fedorov, A S Jensen, N T Zinner, “Borromean ground state of fermions in two dimensions”, J. Phys. B: At. Mol. Opt. Phys., 47:18 (2014), 185302
Yusuke Nishida, Shina Tan, “Liberating Efimov Physics from Three Dimensions”, Few-Body Syst, 51:2-4 (2011), 191
A. S. Jensen, K. Riisager, D. V. Fedorov, E. Garrido, “Structure and reactions of quantum halos”, Rev. Mod. Phys., 76:1 (2004), 215
E. Nielsen, D. V. Fedorov, A. S. Jensen, “Three-body halos in two dimensions”, Phys. Rev. A, 56:4 (1997), 3287
Citation in format AMSBIB
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