
This article is cited in 5 scientific papers (total in 5 papers)
Representation of free solutions for Schrödinger equations with strongly singular concentrated potentials
Yu. M. Shirokov^{}
Abstract:
A new representation is obtained for the Schrödinger equation constructed and solved in the author's earlier paper [1] for threedimensional motion of a particle in the field of a strongly singular concentrated potential. In the new representation, the Schrödinger equation becomes free but the wave functions of the bound states have exponential growth at infinity. The transition to the new representation is linear but contains a procedure of analytic continuation, which makes it a transformation that does not possess a kernel
and does not exist in the complete Hilbert space. It is shown that, using the new
representation, one can readily obtain the complete solution of the original Schrödinger equation. The new “freesolution representation” is used to obtain the complete solution to the quantum problem of the motion of a particle in the field of a centrally symmetric concentrated potential that acts in states with $l\ne0$. Positivity of the metric has not been verified for the obtained solution. The possibility of applying the method to the quantum problem of several bodies with concentrated twobody interactions is noted.
Full text:
PDF file (1366 kB)
References:
PDF file
HTML file
English version:
Theoretical and Mathematical Physics, 1981, 46:3, 191–196
Bibliographic databases:
Received: 16.04.1980
Citation:
Yu. M. Shirokov, “Representation of free solutions for Schrödinger equations with strongly singular concentrated potentials”, TMF, 46:3 (1981), 291–299; Theoret. and Math. Phys., 46:3 (1981), 191–196
Citation in format AMSBIB
\Bibitem{Shi81}
\by Yu.~M.~Shirokov
\paper Representation of free solutions for Schr\"odinger equations with strongly singular concentrated potentials
\jour TMF
\yr 1981
\vol 46
\issue 3
\pages 291299
\mathnet{http://mi.mathnet.ru/tmf2332}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=622509}
\zmath{https://zbmath.org/?q=an:0458.350850486.35070}
\transl
\jour Theoret. and Math. Phys.
\yr 1981
\vol 46
\issue 3
\pages 191196
\crossref{https://doi.org/10.1007/BF01032724}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MN84000001}
Linking options:
http://mi.mathnet.ru/eng/tmf2332 http://mi.mathnet.ru/eng/tmf/v46/i3/p291
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:

I. S. Tsirova, Yu. M. Shirokov, “Quantum deltalike potential acting in the $P$ state”, Theoret. and Math. Phys., 46:3 (1981), 203–206

I. S. Tsirova, “Singular potentials in a problem with noncentral interaction”, Theoret. and Math. Phys., 51:3 (1982), 561–563

G. K. Tolokonnikov, “Differential rings used in Shirokov algebras”, Theoret. and Math. Phys., 53:1 (1982), 952–954

Yu. G. Shondin, “Generalized pointlike interactions in $R_3$ and related models with rational $S$ matrix II. $l=1$”, Theoret. and Math. Phys., 65:1 (1985), 985–992

B. S. Pavlov, A. A. Shushkov, “The theory of extentions and zeroradius potentials with internal structure”, Math. USSRSb., 65:1 (1990), 147–184

Number of views: 
This page:  180  Full text:  74  References:  13  First page:  1 
