  We study the scattering problem, the Sturm-Liouville problem and the spectral
problem with periodic or skew-periodic boundary conditions for the
one-dimensional Schr\"odinger equation with an $n$-cell (finite periodic)
potential. We give explicit upper and lower bounds for the distribution
functions of discrete spectrum for these problems. For the scattering problem
we give, besides, explicit upper and lower bounds for the distribution function
of discrete spectrum for the case of potential consisting of $n$ not
necessarily identical cells. For the scattering problem some results about
transmission resonances are obtained.
