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TMF, 1984, Volume 60, Number 3, Pages 423–431 (Mi tmf5356)  

Inversion transformation in the Schrödinger equation

Yu. N. Demkov, N. V. Semenova


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.

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English version:
Theoretical and Mathematical Physics, 1984, 60:3, 914–920

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Received: 14.10.1983

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
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\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://www.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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984AEF5000009}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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