Calculating the width of an ultranarrow quantum resonance

A reliable way of calculating the width, F, of an extremely narrow quantum resonance is suggested. The proposed method is based on expanding the Jost function in the Taylor series around the real resonance energy, Er, and looking for its zero at the nearby complex point Er - iF /2. The coefficients of such an expansion can be obtained by solving a set of coupled differential equations. Using two simple exactly solvable models, it is demonstrated that the method is efficient and accurate.