BACK-ROTATION OF THE WAVE-FUNCTION IN THE COMPLEX SCALING METHOD

The complex resonance eigenvalue can easily be obtained by scaling the internal coordinates of the Hamiltonian by a complex factor since then the resonance eigenfunction, is square integrable. The back-transformation of however, yields the exact eigenfunction of the original Hamiltonian only when is given in closed form. We show here that in the case when a basis-set method is invoked, even if the limn is the exact solution of the transformed problem, the n limit of the back-rotated n may produce a divergent wave function. Our numerical examples suggest that the quality of approximation in the back-rotated wave function strongly depends on the basis set. © 1990 The American Physical Society.