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Based on the Sum-over-Paths approach of Richard Feynman, an integrationmethod for calculating wave phase vectors is derived. The diffraction andinterference patterns of various slit masks can be calculated from such phasevectors. The results obtained match with those computed using the more complexFresnel integrals. Babinet's principle for phases is presented for the firsttime. As an example, the diffraction pattern of a double slit can also becalculated by subtracting the phase vectors of a smaller slit from those of alarger one. This method is also demonstrated by using a diffraction calculationtool when an obstacle is positioned behind a double slit. The approach of phasevector integration is expanded to calculate the quantum probability current.Based on the Hamilton-Jacobi- and the stationary Schr\"odinger- equation, thequantum probability current is calculated and its continuity is shown. Thetime-dependent differential equation of the probabilty current velocity isnumerically solved. For a large number of integrations it is statisticallyshown that the distribution of the flux per area is consistent with theprobability density profile. The quantum probability current is also simulatedfor photons traversing an asymmetrical double slit and the special results arediscussed.

Feynman's Sum-over-Paths method applied in wave optics and for calculating the quantum probability current