Evaluation of partial widths and branching ratios from resonance wave functions

A quantum system in a given resonance state has different open channels for decay. Partial widths are the decay rates of the resonance (metastable) state into the different open channels. Here we present a rigorous derivation of the partialwidths from the solution of a time-dependent Schr̈odinger equationwith outgoing boundary conditions. We show that the sum of the partial widths obtained from the resonance wave function is equal to the total width. The difference with respect to previous studies on partial widths and branching ratios is discussed.