Square well analysis shows Breit-Wigner poles are not eigenvalues and lead to growing spatial waves; PT symmetry gives conjugate pairs E∓=E2∓iΓ2 with stable amplitudes and one physical resonance.
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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.
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Critique of Breit-Wigner resonance scattering
Square well analysis shows Breit-Wigner poles are not eigenvalues and lead to growing spatial waves; PT symmetry gives conjugate pairs E∓=E2∓iΓ2 with stable amplitudes and one physical resonance.
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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.