We are interested in the nature of the spectrum of the onedimensional Schrödinger
operator
$$\frac{{d}^{2}}{d{x}^{2}}Fx+\sum _{n\in \mathbb{Z}}{g}_{n}\delta (xn)\phantom{\rule{1em}{0ex}}\text{in}{L}^{2}(\mathbb{R})$$ 
with
$F>0$
and two different choices of the coupling constants
${\{{g}_{n}\}}_{n\in \mathbb{Z}}$. In the first model,
${g}_{n}\equiv \lambda $, and we prove
that if
$F\in {\pi}^{2}\mathbb{Q}$ then the
spectrum is
$\mathbb{R}$ and
is furthermore absolutely continuous away from an explicit discrete set of points. In the second
model, the
${g}_{n}$
are independent random variables with mean zero and variance
${\lambda}^{2}$. Under certain
assumptions on the distribution of these random variables, we prove that almost surely the spectrum
is
$\mathbb{R}$ and it is dense pure
point if
$F<\frac{1}{2}{\lambda}^{2}$ and purely
singular continuous if
$F>\frac{1}{2}{\lambda}^{2}$.
