  Most recently, orbital-selective quantum well states of $d$ electrons have
been experimentally observed in SrVO$_3$ ultrathin films [K. Yoshimatsu et.
al., Science 333, 319 (2011)] and SrTiO$_3$ surfaces [A. F. Santander-Syro et.
al., Nature 469, 189 (2011)]. Hitherto, one tries to explain these experiments
by a nearly free electron (NFE) model, an approach widely used for delocalized
electrons in semiconductor heterostructures and simple metal films. We show
that a tight binding (TB) model is more suitable for describing
heterostructures with more localized $d$ electrons. In this paper, we construct
from first principles simple TB models for perovskite oxide heterostructures
and surfaces. We show that the TB model provides a simple intuitive physical
picture and yields, already with only two parameters, quantitatively much more
reliable results, consistent with experiment.
