"Quantum Foam" causes Wave Fxn spreading ?

When a photon Wave Function ("Wave Packet") encounters a partially-silvered mirror, it bifurcates, into two Wave Functions -- one "transmitted" wave, and one "reflected" wave. More generally, quantum waves always split, when encountering spatially sharp potential barriers.

Now, considering the case of a fundamental point-like particle (e.g., electron), this "splitting" of Wave Functions, is qualitatively similar, to the "spreading" of Wave Functions -- which amounts to the successive splittings, in every direction, of the original delta-function-like, point-like particle, position eigenstate. What then is similar, between (1) a photon wave encountering a partially-silvered mirror, and "splitting"; and (2) an electron wave, in empty space, "spreading" ?

Is this where the concept of "quantum foam" enters the picture? Is "empty space" actually filled with virtual particles, whose interactions with actual matter perpetually perturb the same, amounting to myriad "potential barrier encounters", each one of which further "splits" the ever-splitting-and-so-spreading Wave Function ?