The time-dependent quantum-mechanical description of molecular photodissociation processes is briefly reviewed. A new easily implementable method for the calculation of partial cross-sections to produce specific fragment quantum states is presented. The equivalence of the partial cross-sections calculated using these time-dependent quantum-mechanical methods to those calculated using standard time-independent quantum theory is explicitly demonstrated. Sample calculations using a model potential-energy surface for a system having physical parameters corresponding to the H₂S molecule are presented. The power of the method is clearly demonstrated by explicitly showing, for this model system, how a single time-dependent calculation yields the partial photodissociation cross-sections for all photon energies. We furthermore point out the suitability of modern parallel computing techniques in connection with such methods.