  Eigenspectra of a spinless quantum particle trapped inside a rigid,
rectangular, two-dimensional (2D) box subject to diverse inner potential
distributions are investigated under hermitian, as well as non-hermitian
antiunitary $\mathcal{PT}$ (composite parity and time-reversal) symmetric
regimes. Four sectors or "stripes" inscribed in the rigid box comprising
contiguously conjoined parallel rectangular segments with one side equaling the
entire width of the box are studied. The stripes encompass piecewise constant
potentials whose exact, complete energy eigenspectrum is obtained employing
matrix mechanics. Various striped potential compositions, viz. real valued ones
in the hermitian regime as well as complex, non-hermitian but $\mathcal{PT}$
symmetric ones are considered separately and in conjunction, unraveling among
typical lowest lying eigenvalues, retention and breakdown scenarios engendered
by the $\mathcal{PT}$ symmetry, bearing upon the strength of non-hermitian
sectors. Some states exhibit a remarkable crossover of symmetry `making' and
`breaking': while a broken $\mathcal{PT}$ gets reinstated for an energy level,
higher levels may couple to continue with symmetry breaking. Further, for a
charged quantum particle a $\mathcal{PT}$ symmetric electric field, furnished
with a striped potential backdrop, also reveals peculiar retention and
breakdown $\mathcal{PT}$ scenarios. Depictions of prominent probability
redistributions relating to various potential distributions both under
norm-conserving unitary regime for hermitian Hamiltonians and non-conserving
ones post $\mathcal{PT}$ breakdown are presented.
