On some bound and scattering states associated with the cosine kernel

Abstract

It is explained how to provide self-adjoint operators having scattering states forming a multiplicity one continuum and bound states whose corresponding eigenvalues have an asymptotic density equivalent to the one of the zeros of the Riemann zeta function. It is shown how this can be put into an integro-differential form of a type recently considered by Sierra.

18 pages

References in corpus (2)

• H = x p with interaction and the Riemann zeros
• Spacetime causality in the study of the Hankel transform