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 TMF, 1988, Volume 74, Number 3, Pages 331–344 (Mi tmf4422)

Quantum-mechanical models in $R_n$ associated with extensions of the energy operator in a Pontryagin space

Yu. G. Shondin

Abstract: The paper describes self-adjoint extensions of the operator $H_0=-\Delta$ from the Hilbert space $L_2(R_n)$ to a certain Pontryagin space generated by “interactions” represented by generalized functions. Hamiltonians of quantum-mechanical models are obtained by restricting such extensions to positive invariant subspaces.

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English version:
Theoretical and Mathematical Physics, 1988, 74:3, 220–230

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Revised: 01.10.1986

Citation: Yu. G. Shondin, “Quantum-mechanical models in $R_n$ associated with extensions of the energy operator in a Pontryagin space”, TMF, 74:3 (1988), 331–344; Theoret. and Math. Phys., 74:3 (1988), 220–230

Citation in format AMSBIB
\Bibitem{Sho88} \by Yu.~G.~Shondin \paper Quantum-mechanical models in~$R_n$ associated with extensions of the energy operator in a~Pontryagin space \jour TMF \yr 1988 \vol 74 \issue 3 \pages 331--344 \mathnet{http://mi.mathnet.ru/tmf4422} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=953297} \zmath{https://zbmath.org/?q=an:0685.46047} \transl \jour Theoret. and Math. Phys. \yr 1988 \vol 74 \issue 3 \pages 220--230 \crossref{https://doi.org/10.1007/BF01016615} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1988U172700002} 

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