1. Discreteness. 

Another of the particlelike properties of matter is its discreteness.  A classical electron or proton or atom is a discrete (localized) unit of matter that carries a discrete amount of  mass, energy, momentum spin and charge.  But this particlelike discreteness is also accounted for in quantum mechanics.  Each “single particle” wave function, whether it is a lightlike wave function, an electronlike wave function, or an atomiclike wave function, carries a discrete amount of energy, momentum and charge, with exactly the same consequences as would occur under a particle picture.

2. Discreteness and the Photoelectric Effect. 

If we consider the photoelectric effect, for example, the beam of light that impinges on the metal consists of a product of individual photonlike wave functions.  Each of these individual wave functions imitates the degrees of freedom that we normally associate with a particle.  Thus the effects that we classically attribute to discrete particles—a discrete number of photons, for example, instead of a continuum of light—are accounted for in quantum mechanics by the discrete product form of the wave function. 

3. Discreteness for Electronlike Wave Functions. 

The same holds for the beam of “electrons” that is shot from the electrode to the screen in your television set.  The beam actually consists of a discrete product of electronlike wave functions, each of which carries a discrete amount of energy, momentum and charge.  Thus it is not necessary to assume there are discrete, objectively existing particles, for each of the terms in the discrete product of electronlike wave functions acts just like a particle.

4. The Atomic Graininess of Matter. 

And the same holds for the atomic “graininess” of matter because (neglecting interactions) the total wave function is a discrete product of individual atomic wave functions, each of which acts like a particle.