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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

Bibliographic databases:

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://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}