This is a pretty fundamental mischaracterization of quantum mechanics. Whether one uses Dirac's Bras and Kets notation or simply represents the wavefunction like any other probability funtion, it remains a
notational schema. For many, this formalism actually describes a probabilistic physical reality, For others, it doesn't. The formalism is an extension of the classical axiomized probability triplet <Ω,
F,p>, where the probability space is replaced with Hilbert space, the probability algrebra with a Lie algebra (the algebra of events in QM forms a lattice), and the probability measure is replaced by the wavefunction, making the following triplet:
The measurement problem (among other things), creates problems for anyone seeking to take quantum algebras, Riemannian geometry, and other formalisms used in QM as descriptions of the reality. A simplistic analogy would be the comparison between arithmetic and reality: 4 + 2 = 6, but how does one add 4 books to 2 apples, and what does one get: 8 objects, or hundreds of pages and a snack?
Even under the Copenhagen interpretation, the quoted description of waves and particles isn't accurate. And as physicists are still arguing over whether the universe is fundamentally discrete, over the existence of particles and particles with 0-volumes, etc., saying much of anything about the "physical characterizations" of particles is to be overly optimistic.
In particular though, the point about waves and particles and quantum physics is not that a "wave happens with particles" but that the classical distinction between the two doesn't hold up.