Title: Controlled trapping of single particle states on a periodic substrate by deterministic stubbing,
Abstract: A periodic array of atomic sites, described within a tight binding formalism
is shown to be capable of trapping electronic states as it grows in size and
gets stubbed by an atom or an atomic clusters from a side in a deterministic
way. We prescribe a method based on a real space renormalization group method,
that unravels a subtle correlation between the positions of the side coupled
atoms and the energy eigenvalues for which the incoming particle finally gets
trapped. We discuss how, in such conditions, the periodic backbone gets
transformed into an array of infinite quantum wells in the thermodynamic limit.
We present a case here, where the wells have a hierarchically distribution of
widths, hosing standing wave solutions in the thermodynamic limit.