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Teoreticheskaya i Matematicheskaya Fizika, 1984, Volume 60, Number 3, Pages 423–431 (Mi tmf5356)  
This article is cited in 1 scientific paper (total in 1 paper)

Inversion transformation in the Schrödinger equation

Yu. N. Demkov, N. V. Semenova
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Abstract: The equivalence of Schrödinger equations with different types of potentials is established on the basis of an inversion transformation. It is shown that at zero energy the equation with a spherical potential is equivalent to the equation with an axisymmetric potential of special form. Exact solutions are obtained to problems of the motion of a particle with zero total energy in the field of two “fish-eye” potentials and also in the field of a potential with two Coulomb singularities.
Received: 14.10.1983
English version:
Theoretical and Mathematical Physics, 1984, Volume 60, Issue 3, Pages 914–920
DOI: https://doi.org/10.1007/BF01017894
Bibliographic databases:
Language: Russian
Citation: Yu. N. Demkov, N. V. Semenova, “Inversion transformation in the Schrödinger equation”, TMF, 60:3 (1984), 423–431; Theoret. and Math. Phys., 60:3 (1984), 914–920
Citation in format AMSBIB
\Bibitem{DemSem84}
\by Yu.~N.~Demkov, N.~V.~Semenova
\paper Inversion transformation in the Schr\"{o}dinger equation
\jour TMF
\yr 1984
\vol 60
\issue 3
\pages 423--431
\mathnet{http://mi.mathnet.ru/tmf5356}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=768170}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 60
\issue 3
\pages 914--920
\crossref{https://doi.org/10.1007/BF01017894}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984AEF5000009}
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  • https://www.mathnet.ru/eng/tmf5356
  • https://www.mathnet.ru/eng/tmf/v60/i3/p423
    • This publication is cited in the following 1 articles:
    1. Radosław Szmytkowski, “Green's function for the wavized Maxwell fish-eye problem”, J. Phys. A: Math. Theor., 44:6 (2011), 065203  crossref
    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
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    Abstract page:656
    Full-text PDF :250
    References:59
    First page:1
     
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