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Title: A product formula for the eigenfunctions of a quartic oscillator
Authors: Hallnas, Martin
Langmann, Edwin
Keywords: Asymptotic expansions
Kernel functions
Product formula
Quartic oscillator
Issue Date: 2015
Publisher: © Elsevier
Citation: HALLNAS, M. and LANGMANN, E., 2015. A product formula for the eigenfunctions of a quartic oscillator. Journal of Mathematical Analysis and Applications, 426 (2), pp. 1012-1025.
Abstract: We consider the Schrödinger operator on the real line with an even quartic potential. Our main result is a product formula of the type. ψk(x)ψk(y)=∫Rψk(z)K(x,y,z)dz for its eigenfunctions ψk. The kernel function K is given explicitly in terms of the Airy function Ai(x), and it is positive for appropriate parameter values. As an application, we obtain a particular asymptotic expansion of the eigenfunctions ψk.
Description: This article was published in Journal of Mathematical Analysis and Applications [© Elsevier] and the definitive version is available at: http://dx.doi.org/10.1016/j.jmaa.2015.02.014
Sponsor: This work was supported by the Göran Gustafsson Foundation (grant No. GGS 1221) and the Swedish Research Council (VR) under contract No.621-2010-3708.
Version: Accepted for publication
DOI: 10.1016/j.jmaa.2015.02.014
URI: https://dspace.lboro.ac.uk/2134/17028
Publisher Link: http://dx.doi.org/10.1016/j.jmaa.2015.02.014
ISSN: 0022-247X
Appears in Collections:Published Articles (Maths)

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