In quantum mechanics, how does the probability amplitude of a state vector affect the outcome of quantum interference in a two-slit experiment?

The probability amplitude is a complex number that tells how strongly a particle’s state is present at each slit. When the particle reaches the screen, the amplitudes from the two slits are added together, and the phase of each complex number decides whether the sum is large or small. If the amplitudes are in phase, their magnitudes add and the interference is constructive, producing a bright fringe; if they are out of phase, they cancel and a dark fringe appears. For example, if the amplitudes from both slits are equal and have the same phase, the center of the pattern will be a bright spot, while a half‑wave phase shift turns that spot into a dark line. Thus, the size and phase of the probability amplitudes directly shape the interference pattern observed in the two‑slit experiment.