On detection and representation of resonances by the method of stabilization

We present an explanation of why the stabilization method works in the detection and representation of resonances. This explanation is based on the fact that a variational approach provides a coarse grain discretization of the continuum which privileges particular regions of configuration space. We illustrate how the stability of eigenvalues corresponding to resonances results simply from the properties of the Heisenberg representation of the variational wavefunctions. Conclusions are drawn as to the properties that basis sets should have to detect resonances and to reproduce them accurately.