I am sorry, but this response ["particles are also waves... waves of existence..."] strikes me as unrelated concepts without coherent meaning.
The latter repeats a common confusion. First, you can't write the Schrodinger wave (probability) equation for the photon because it has zero rest mass. Second, the wave of the photon is real and actual; Maxwell's equations describe it and it registers on an oscilloscope (which the Schrodinger wave will never do). Third, you are mixing a physical entity (a photon or electron) with a mathematical/calculated entity (the Schrodinger equation) and asking the latter to influence the path of the former. This makes the Schrodinger equation prescriptive rather than descriptive. Some interpretations argue for the physical reality of the probability wave (Objective Collapse) but they have not received much support
So if single photons pass through a double slit at separate time intervals and yet still form a diffraction pattern with their individual "impacts" then each photon must be interfering with itself through the double slit as the above quote indicates. This says the photon is a wave since only waves can produce interference patterns. But each photon registers at a space point so does this prove it is a particle when passing through the slit and before it has terminated? It does not; it merely says that whatever the photon is, it registers/terminates upon matter at a space point. Keep two things in mind here: 1. when the photon registers on matter at a space point it has already terminated and ceases to be a photon (although some photon energy may re-emit as a new photon); 2. we are all slaves of classical physics concepts and we think that anything moving through space and "impacting" matter at a point must be a projectile (particle). There is no hard proof of this assumption; there could be real entities we do not know about that collapse at a space point.
An interesting reinterpretation of photon termination (Wave-Particle Duality) argues that when photons terminate upon matter their space-dispersed, stored (potential) mass collapses at a space point thus simulating particle impact. This potential mass could be the entity "we do not know about."
One hundred years of debate and we are still searching for an answer...