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 TMF, 1999, Volume 120, Number 3, Pages 473–481 (Mi tmf791)

Recurrent calculations of multipole matrix elements

S. Yu. Slavyanov

Saint-Petersburg State University

Abstract: We propose a new method for calculating multipole matrix elements between wave eigenfunctions of the one-dimensional Schrödinger equation. The method is based on the transition to the auxiliary third- and fourth-order equations, to which an analogue of the Laplace transform is then applied. The resulting recursive procedure allows us to evaluate matrix elements starting with a number of eigenvalues that are assumed to be known and several basis matrix elements. As an example, we consider the multipole matrix elements between the wave functions of the harmonic and nonharmonic oscillators.

DOI: https://doi.org/10.4213/tmf791

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English version:
Theoretical and Mathematical Physics, 1999, 120:3, 1213–1219

Bibliographic databases:

Citation: S. Yu. Slavyanov, “Recurrent calculations of multipole matrix elements”, TMF, 120:3 (1999), 473–481; Theoret. and Math. Phys., 120:3 (1999), 1213–1219

Citation in format AMSBIB
\Bibitem{Sla99} \by S.~Yu.~Slavyanov \paper Recurrent calculations of multipole matrix elements \jour TMF \yr 1999 \vol 120 \issue 3 \pages 473--481 \mathnet{http://mi.mathnet.ru/tmf791} \crossref{https://doi.org/10.4213/tmf791} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1737360} \zmath{https://zbmath.org/?q=an:0967.81009} \transl \jour Theoret. and Math. Phys. \yr 1999 \vol 120 \issue 3 \pages 1213--1219 \crossref{https://doi.org/10.1007/BF02557244} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000084178900009} 

• http://mi.mathnet.ru/eng/tmf791
• https://doi.org/10.4213/tmf791
• http://mi.mathnet.ru/eng/tmf/v120/i3/p473

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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:
1. Slavyanov S.Y., “Multipole matrix elements”, International Seminar Day on Diffraction, Proceedings, 1999, 189–195
2. Slavyanov S.Y., “The equation for a product of solutions of two second-order linear ODEs”, Day on Diffraction - Millennium Workshop, Proceedings, 2000, 168–171
3. Papshev V.Y., “Analytical and numerical calculation of multipole matrix elements”, Day on Diffraction 2001, Proceedings, 2001, 211–214
4. S. Yu. Slavyanov, “Equation for a Product of Solutions of Two Different Schrödinger Equations”, Theoret. and Math. Phys., 136:3 (2003), 1251–1257
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