The versatile and exactly solvable Scarf II potential has been predicting, confirming and demonstrating interesting phenomena in complex PT-symmetric sector, most impressively. However, for the non-PT-symmetric sector, it has gone underutilised. Here, we present the most simple analytic forms for the scattering coefficients \((T(k),R(k),|\det S(k)|)\). On the one hand, these forms demonstrate earlier effects and confirm the recent ones. On the other hand, they make new predictions – all simple and analytical. We show the possibilities of both self-dual and non-self-dual spectral singularities (NSDSS) in two non-PT sectors (potentials). The former one is not accompanied by time-reversed coherent perfect absorption (CPA) and gives rise to the parametrically controlled splitting of spectral singularity (SS) into a finite number of complex conjugate pairs of eigenvalues (CCPEs). NSDSS behave just oppositely: CPA but no splitting of SS. We demonstrate a one-sided reflectionlessness without invisibility. Most importantly, we bring out a surprising coexistence of both real discrete spectrum and a single SS in a fixed potential. Nevertheless, so far, the complex Scarf II potential is not known to be pseudo-Hermitian (\(\eta ^{-1} H\eta =H^\dagger \)) under a metric of the type \(\eta (x)\).

令人印象深刻的是，多功能且可完全解决的Scarf II潜力已经在复杂的PT对称扇区中预测，证实和演示了有趣的现象。但是，对于非PT对称行业，它的利用不足。在这里，我们给出散射系数\（（T（k），R（k），| \ det S（k）|）\）的最简单解析形式。一方面，这些形式证明了较早的作用并证实了最近的作用。另一方面，他们做出了新的预测-既简单又分析。我们展示了在两个非PT扇区（电势）中自对偶和非对偶频谱奇点（NSDSS）的可能性。前一种不伴随时间反转的相干完美吸收（CPA），并且引起了光谱奇异性（SS）的参量控制分裂为有限数量的特征值复共轭对（CCPE）。NSDSS的行为恰恰相反：CPA，但SS没有分裂。我们展示了无隐形的单面无反射性。最重要的是，我们带出了令人惊讶的真实离散频谱与固定电位下单个SS的共存。不过到目前为止\（\ eta ^ {-1} H \ eta = H ^ \ dagger \）），其度量标准为\（\ eta（x）\）。