  We present the quantum mechanics problem of the one-dimensional Schroedinger
equation with the trigonometric Rosen-Morse potential. This potential is of
possible interest to quark physics in so far as it captures the essentials of
the QCD quark-gluon dynamics and (i) interpolates between a Coulomb-like
potential (associated with one-gluon exchange) and the infinite wall potential
(associated with asymptotic freedom), (ii) reproduces in the intermediary
region the linear confinement potential (associated with multi-gluon
self-interactions) as established by lattice QCD calculations of hadron
properties. Moreover, its exact real solutions given here display a new class
of real orthogonal polynomials and thereby interesting mathematical entities in
their own.
