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A product formula for the eigenfunctions of a quartic oscillator
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
2015 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 426, no 2, 1012-1025 p.Article in journal (Refereed) Published
Abstract [en]

We consider the Schrodinger operator on the real line with an even quartic potential. Our main result is a product formula of the type psi(k)(x)psi(k)(y) = integral(R) psi(k)(z)K(x,y, z)dz for its eigenfunctions psi(k). 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 psi(k).

Place, publisher, year, edition, pages
2015. Vol. 426, no 2, 1012-1025 p.
Keyword [en]
Quartic oscillator, Product formula, Kernel functions, Asymptotic expansions
National Category
URN: urn:nbn:se:kth:diva-165187DOI: 10.1016/j.jmaa.2015.02.014ISI: 000351249300026ScopusID: 2-s2.0-84923629557OAI: diva2:810965

QC 20150508

Available from: 2015-05-08 Created: 2015-04-24 Last updated: 2015-05-08Bibliographically approved

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Langmann, Edwin
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