A Power Series Representation for the Characteristic Equation of Gamow-Siegert Eigenstates

In this work we consider a quantum system described by a stationary Schrödinger equation and obtain an explicit representation for the characteristic equation of its Gamow-Siegert eigenstates in the form of a power series of the energy parameter. This representation is valid for both analytical or numerical calculations. We show that determining resonances reduces to calculating the roots of a polynomial equation. The effectiveness of this approach is demonstrated through several numerical examples. (paper)