Despite being presented as one of the fundamental results of Quantum Mechanics in practically every textbook, I realized this morning that I don't understand deeply how Quantum Mechanics predicts the double slit experiment.
The best explanation I have found seems to be closely related to the path integral formulation (e.g., since there are to a good approximation only two paths that a particle can take, the amplitudes due to these two paths add/interfere).
However, I am interested in how one could go about deriving the result using the methods taught in an introductory quantum mechanics course: defining a potential, solving the Schrodinger equation, using the generalized statistical interpretation, etc. Is there a simple way to see it from this angle? Or is this a result best left to understanding via the path integral?