  Based on the Sum-over-Paths approach of Richard Feynman, an integration
method for calculating wave phase vectors is derived. The diffraction and
interference patterns of various slit masks can be calculated from such phase
vectors. The results obtained match with those computed using the more complex
Fresnel integrals. Babinet's principle for phases is presented for the first
time. As an example, the diffraction pattern of a double slit can also be
calculated by subtracting the phase vectors of a smaller slit from those of a
larger one. This method is also demonstrated by using a diffraction calculation
tool when an obstacle is positioned behind a double slit. The approach of phase
vector integration is expanded to calculate the quantum probability current.
Based on the Hamilton-Jacobi- and the stationary Schr\"odinger- equation, the
quantum probability current is calculated and its continuity is shown. The
time-dependent differential equation of the probabilty current velocity is
numerically solved. For a large number of integrations it is statistically
shown that the distribution of the flux per area is consistent with the
probability density profile. The quantum probability current is also simulated
for photons traversing an asymmetrical double slit and the special results are
discussed.
