  We introduce a one-dimensional PT-symmetric system, which includes the cubic
self-focusing, a double-well potential in the form of an infinitely deep
potential box split in the middle by a delta-functional barrier of an effective
height epsilon, and constant linear gain and loss, gamma, in each half-box. The
setting may be realized in microwave photonics. Using numerical methods, we
construct PT-symmetric and antisymmetric modes, which represent, respectively,
the system's ground state and first excited state, and identify their
stability. When they are unstable, the instability leads to blowup, except for
the case of epsilon = 0, when an unstable symmetric mode transforms into a
weakly oscillating breather, and an unstable antisymmetric mode relaxes into a
stable symmetric one. At epsilon > 0, the stability area is much larger for the
PT-antisymmetric state than for its symmetric counterpart. The stability areas
shrink with with increase of the total power, P. In the linear limit, which
corresponds to P --> 0, the stability boundary is found in an analytical form.
The stability area of the antisymmetric state originally expands with the
growth of gamma, and then disappears at a critical value of gamma.
