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A product formula for the eigenfunctions of a quartic oscillator

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 approp...

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Bibliographic Details
Main Authors: Martin Hallnas, Edwin Langmann
Format: Default Article
Published: 2015
Subjects:
Online Access:https://hdl.handle.net/2134/17028
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