Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schrödinger equation
AbstractThe phenomenon of the birth of an isolated quantum bound state at the lower edge of the continuum is studied for a particle moving along a discrete real line of coordinates x∈Z. The motion is controlled by a weakly nonlocal 2J-parametric external potential V which is non-Hermitian but PT symmetric. The model is found exactly solvable. The bound states are interpreted as Sturmians. Their closed-form definitions are presented and discussed up to J=7.