  Exact solvability of two typical examples of the discrete quantum mechanics,
i.e. the dynamics of the Meixner-Pollaczek and the continuous Hahn polynomials
with full parameters, is newly demonstrated both at the Schroedinger and
Heisenberg picture levels. A new quasi exactly solvable difference equation is
constructed by crossing these two dynamics, that is, the quadratic potential
function of the continuous Hahn polynomial is multiplied by the constant phase
factor of the Meixner-Pollaczek type. Its ordinary quantum mechanical
counterpart, if exists, does not seem to be known.
