Potential separable expansion method and its relation to the Siegert method and the complex rotation technique

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Abstract
It is demonstrated with the example of an atomic-physical model potential that the performance of the approximation method for determining resonances, based on a separable expansion of the potential (PSE method), is comparable with that of the Siegert method and of the complex rotation technique. In fact, it is shown that when converged, the PSE method with a real harmonic-oscillator wave-function basis is equivalent to the complex variational method with a trial function set containing a Siegert function; if the potential is dilation analytic the PSE method with a complex oscillator wave-function basis amounts to solving the complex rotated Schrödinger equation with the real PSE method and rotating back the obtained wave function. The results are tested against those yielded by direct numerical integration and against the complex virial theorem.