  Recently, a class of PT-invariant quantum mechanical models described by the
non-Hermitian Hamiltonian $H=p^2+x^2(ix)^\epsilon$ was studied. It was found
that the energy levels for this theory are real for all $\epsilon\geq0$. Here,
the limit as $\epsilon\to\infty$ is examined. It is shown that in this limit,
the theory becomes exactly solvable. A generalization of this Hamiltonian,
$H=p^2+x^{2M}(ix)^\epsilon$ (M=1,2,3,...) is also studied, and this
PT-symmetric Hamiltonian becomes exactly solvable in the large-\epsilon limit
as well. In effect, what is obtained in each case is a complex analog of the
Hamiltonian for the square well potential. Expansions about the large-\epsilon
limit are obtained.
