Zero width resonance (spectral singularity) in a complex PT-symmetric potential

Details Zero width resonance (spectral singularity) in a complex PT-symmetric potential Zero width resonance (spectral singularity) in a complex PT-symmetric potential

2009-08-20

arxiv.org/abs/0908.2876v1

Physics

Quantum Physics

No figures, 4 pages

Scientific paper

We show that the complex PT-Symmetric potential, $V(x)=-V_1 {sech}^2x + iV_2
{sech}x ~\tanh x, $, entails a single zero-width resonance (spectral
singularity) when $V_1+|V_2|=4n^2+4n+{3\over 4}(n=1,2,3.., |V_2|>|V_1|+
{{sgn}(V_1) \over 4})$ and the positive resonant energy is given as $E_*={1
\over 4}[|V_2|-(1/4+V_1)]$.

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