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A general method, which we call the potential $S$-matrix pole method, isdeveloped for obtaining the $S$-matrix pole parameters for bound, virtual andresonant states based on numerical solutions of the Schr\"odinger equation.This method is well-known for bound states. In this work we generalize it forresonant and virtual states, although the corresponding solutions increaseexponentially when $r\to\infty$. Concrete calculations are performed for the$1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance$^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and$^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. Wealso demonstrate that in the case the broad resonances their energy and widthcan be found from the fitting of the experimental phase shifts using theanalytical expression for the elastic scattering $S$-matrix. We compare the$S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in${}^{15}{\rm F}$

Bound, virtual and resonance $S$-matrix poles from the Schr\"odinger equation