A product formula for the eigenfunctions of a quartic oscillator

作者：Hallnaes Martin; Langmann Edwin

来源：Journal of Mathematical Analysis and Applications, 2015, 426(2): 1012-1025.

DOI：10.1016/j.jmaa.2015.02.014

• Quartic oscillator
• Product formula
• Kernel functions
• Asymptotic expansions

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).

• 出版日期2015-6-15