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.
Fourth Order Theories Without Ghosts
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abstract
Using the Dirac constraint method we show that the pure fourth-order Pais-Uhlenbeck oscillator model is free of observable negative norm states. Even though such ghosts do appear when the fourth order theory is coupled to a second order one, the limit in which the second order action is switched off is found to be a highly singular one in which these states move off shell. Given this result, construction of a fully unitary, renormalizable, gravitational theory based on a purely fourth order action in 4 dimensions now appears feasible.
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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.