No doubt it's been questioned before so what is the theory or experiment? If there is an experiment.
closed as unclear what you're asking by John Rennie, Kyle Kanos, jinawee, Qmechanic♦ Mar 13 at 15:06
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.
Reading your question and the comments beneath, your use of the term "particle function" has no real meaning.
I think I understand what you are asking, something like... We have proved that waves (light) can act as a particles through the double slit experiment. Is there a method to prove that matter (particles) can act an a wavelike manner?
The answer of course is yes! We have used the particle equivalent of the DS expt. which is electron diffraction. We can shoot a beam of electrons through a diffracting crystal (the lattice of the crystal acts as the slits) and we are able to see a diffraction pattern:
Apologies if this is not the question you're asking.