\begin{document}$^{40}\mathrm{Ca}$\end{document} as an example, we show that the GF results for both bound and resonant single-neutron states are consistent with those obtained by the shooting and scattering matrix methods respectively. Explicitly, three different recipes (GFI, GFII, and GFIII) are used to figure out the energies and widths of resonant states. The GFI method directly reads the resonant energy and width from the calculated density of states after removing the contributions of free particles. The GFII method identifies the resonant states by examining the flip of the density of states, while the GFIII method searches for the resonant states as poles of the modulus of GF on the complex energy plane. It is found that the GFI method is effective for the resonant states with narrow widths. For the resonant states with broad widths, the GFII and GFIII methods are more accurate and effective. We also verified that the energies, widths, and density distributions of resonant states obtained by the GF method exhibit a rather weak dependence on the box size."> Resonant states in the Schrödinger equation solved by the Green's function method -
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