Perfect Transmission Energies |
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We study a quantum-mechanical scattering on potentials with compact support,
particularly perfect transmisson energies (PTEs), i.e. energies for which there is no reflection.
We formulate this as a non-self-adjoint (PT-symmetric) spectral problem.
The animated plots illustrate:
a) the associated non-self-adjoint spectral problem, where the PTEs correspond to intersections of real (before crossing)
energy levels (red full curves) and the dispersion parabola (blue dashed curve),
b) the plot of transmission coefficient |T|2 as a function of energy. PTEs are the peaks touching 1,
c) considered shape of a step-like potential, β3 is the depth of the middle well,
β1=-200 is the depth of the left and right well
d) PTEs (blue balls).
Crossings of energy levels in a) as the middle well depth changes in c) result in creations of complex pairs of eigenvalues.
When the dispersion parabola
approaches the point of complexification, the collisions and mergings of the peaks (with value 1) can be observed in the
|T|2 plot.
Subsequently, a decrease of peaks in the plot b) correspond to the loss of PTEs in plot d).
Details can be found in
Perfect transmission scattering as a PT-symmetric spectral problem
by H. Hernandez-Coronado, D. Krejčiřík, and P. Siegl.
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