关于PT对称复化Scarf II势、谱奇异性的更新以及关于合理扩展超对称伙伴的一些评论
An update on PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally-extended supersymmetric partners
摘要：
重新研究了$\cal PT$对称络合Scarf Ⅱ势$V(x)= - V_1 \sech^{2}x + {\rm i} V_2 \sech x \tanh x$，$V_1>0$，$V_{2}\neq 0$，研究了其耦合参数之间的相互作用.本文通过相应波函数的行为证明了一个孤立的正实能级的存在，并指出了它的一些性质。我们还构造了四个不同的合理扩展的超对称合作伙伴的$V(x)$，这是$\cal PT$ -对称或复杂的非$\cal PT$ -对称根据耦合参数范围。对其中一个合作伙伴的详细研究表明，超对称性保持了$V(x)$谱奇异性的存在。
英文摘要：
The $\cal PT$-symmetric complexified Scarf II potential $V(x)= - V_1 \sech^{2}x + {\rm i} V_2 \sech x \tanh x$, $V_1>0$ , $V_{2}\neq 0$ is revisited to study the interplay among its coupling parameters. The existence of an isolated real and positive energy level that has been recently identified as a spectral singularity or zero-width resonance is here demonstrated through the behaviour of the corresponding wavefunctions and some property of the associated pseudo-norms is pointed out. We also construct four different rationally-extended supersymmetric partners to $V(x)$, which are $\cal PT$-symmetric or complex non-$\cal PT$-symmetric according to the coupling parameters range. A detailed study of one of these partners reveals that SUSY preserves the $V(x)$ spectral singularity existence.
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