Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials

摘要: We derive certain identities satisfied by the left/right-reflection and transmission amplitudes, $R^{l/r}(k)$ $T(k)$, of general ${\cal PT}$-symmetric scattering potentials. use these to give a proof relations, $|T(-k)|=|T(k)|$ $|R^r(-k)|=|R^l(k)|$, conjectured in [Z. Ahmed, J. Phys. A 45 (2012) 032004], establish generalized unitarity relation: $R^{l/r}(k)R^{l/r}(-k)+|T(k)|^2=1$, show that it is common property both real complex The same holds for $T(-k)=T(k)^*$ $|R^r(-k)|=|R^l(k)|$.