  The numerical extraction of resonant states of open quantum systems is
usually a difficult problem. Regularization techniques, such as the mapping to
complex coordinates or the addition of Complex Absorbing Potentials are
typically employed, as they render resonant wavefunctions localized and
therefore normalizable. Physically relevant metastable states have energies
that do not depend on the chosen regularization method. Their identification
therefore involves cumbersome comparisons between multiple regularised
calculations, often performed graphically, which require fine-tuning and
specific intuition to avoid approximated, if not wrong, results. In this
Letter, we define an operator that explicitly measures such invariance, valid
for any arbitrary mapping of spatial coordinates. Resonant states of the system
can eventually simply be identified evaluating the expectation value of this
operator. Our method eases the extraction of resonant states even for numerical
potentials that are difficult to scale to complex coordinates, and avoids the
need for ad hoc complex absorbing potentials. We provide explicit evidence of
our findings discussing one-dimensional case-studies,also in the presence of
external electric fields.
