A new analysis challenges the traditional interpretation of Breit-Wigner resonances in particle scattering, a fundamental concept in particle and nuclear physics. The standard formulation associates these resonances with complex energy poles in the scattering amplitude, identifying them with unstable particles. However, this study, based on solving the scattering problem for a square well, reveals that the description of the scattering phase $\tan\delta_{\rm BW} = \Gamma_1/(E_1-E)$ is not always adequate, and that the resonance width $\Gamma_1$ can be negative, which lacks physical meaning.

The researchers point out that the complex pole energy $E_{\rm BW} = E_1 - i\Gamma_1$ does not represent a real energy eigenvalue, implying that it does not correspond to a physical particle. Furthermore, the spatial wave functions associated with decaying energy states exhibit unacceptable exponential growth. These problems are resolved by considering that, due to antilinear PT symmetry, solutions to the Schrödinger equation for the square well appear in pairs of complex conjugate energies $E_{\mp} = E_2 \mp i \Gamma_2$. Crucially, $E_{-} \neq E_{\rm BW}$.

This new perspective leads to a time-independent probability amplitude that neither grows nor decays, either in time or in space. Most significantly, this formulation predicts a single observable physical resonance, rather than the two that might be inferred from the naive interpretation of complex poles. This work suggests a revision of how unstable resonances are conceptualized and interpreted in various quantum systems, with implications for understanding short-lived particles and scattering processes.