Title Slater sum for the one-dimensional $sech^{2}$ potential in relation to the kinetic energy density Author Howard, I.A. Minguzzi, A. March, N.H. Tosi, M.P. Faculty/Department Faculty of Sciences. Physics Publication type article Publication 2004 New York, N.Y. , 2004 Subject Physics Source (journal) Journal of mathematical physics. - New York, N.Y. Volume/pages 45(2004) :6 , p. 2411-2419 ISSN 0022-2488 ISI 000221658500022 Carrier E Target language English (eng) Full text (Publishers DOI) Affiliation University of Antwerp Abstract In earlier work on the one-dimensional sech(2) potential energy [I. A. Howard and N.H. March, Int. J. Quantum Chem. 91, 119 (2003)] it has been shown that both electron density rho(x) and kinetic energy t(x) are low-order polynomials in the potential V(x), for a small number of bound states. Here all attention is focused on the continuum states for the sech(2) potential with a single bound state. The tool employed is the Slater sum, which satisfies a partial differential equation. This is first solved explicitly for the bound state, and then the solution is generalized to apply to the continuum. Again, considerable simplification is exhibited for this specific choice of potential. A brief discussion is included of a central sech(2)(r) potential. (C) 2004 American Institute of Physics. E-info https://repository.uantwerpen.be/docman/iruaauth/d55261/7794180.pdf http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000221658500022&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000221658500022&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000221658500022&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 Handle