Wave packets / the wave function is described as the probability density function of a particle, implying that the particle exists exactly at any 1 location at a time according to its associated wave function. This does not make sense to me on many levels, and it seems inconsistent with quantum tunneling: in quantum tunneling, a wave packet is partially emitted through a barrier, effectively splitting the wave function into a reflected and emitted components. But if the wave function is truly the probability density function for some particle, then that would mean the particle must be jumping back and forth between the 2 disparate pieces of its wave function, which would mean we would often be observing particles that disappear and reappear all around us. It also does not really clarify the wave particle duality issue either. If, on the other hand, I accept that the wave function is the probability of finding a particle at that location, then this makes more sense in both contexts, because it explains particles as simply some kind of "coagulation" of the waves, which means that everything can be thought of us simply the density of a particular frequency at any point in space which create the illusion of a finite set of particles due to cohesive abilities of the waves. Also, how is the wave function different for different kinds of particles? And is it ever possible for a quantum tunneling to create a different type of particle across the barrier?