Spectral properties of the massless relativistic quartic oscillator (Q1688681)

The authors derive explicit formulae on the spectrum and eigenfunctions of \(H\). Here \(H\) is the specific non-local Schrödinger operator, defined as the sum of the square root of the Laplacian and a quartic potential in one-dimension. In [\textit{J. Lőrinczi} and \textit{J. Małecki}, J. Differ. Equations 253, No. 10, 2846--2871 (2012; Zbl 1272.47063)], the authors obtained explicit formulae for the eigenvalue problem in the case of a quadratic potential and they also gave closed formulae for the Fourier transform of the eigenfunctions in terms of Airy functions. Unlike to this work, the Fourier transforms are expressed in two terms involving the fourth-order Airy function for the case presented this paper.