“Striped” rectangular rigid box with Hermitian and non-Hermitian PT symmetric potentials

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