The square-well Schrödinger equation with real potential exhibits PT symmetry, yielding real bound states and complex-conjugate resonance pairs in scattering, so that antilinearity is more general than Hermiticity.
In that effect the center of a wave packet approaching a well (or barrier) travels on the classical trajectory
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PT symmetry and the square well potential: Antilinear symmetry rather than Hermiticity in scattering processes
The square-well Schrödinger equation with real potential exhibits PT symmetry, yielding real bound states and complex-conjugate resonance pairs in scattering, so that antilinearity is more general than Hermiticity.