In many popular-science texts, and also in some older school textbooks, the mysterious behavior of quantum objects is reduced to the duality of wave and particle.
The impression is conveyed that the indeterminism of quantum mechanics consists in the fact that one cannot predict whether a quantum object will behave as a particle or as a wave in a given experiment.
This is misleading. It is true that the description of quantum objects cannot be reduced to a pure wave or particle model. This is a remarkable fact that contradicts classical notions and must be given due attention in teaching.
The “riddle” of wave-particle duality in this naive form is, however, completely resolved by Born’s probability interpretation (this is discussed in detail in the lesson Probability interpretation and wave function): the wave function obeys wave laws, and the square of its magnitude gives the probability of finding the quantum object at the location in question. For every experiment one can predict unambiguously whether one will find “wave behavior” or “particle behavior”.
The indeterministic element of quantum mechanics lies rather in the fact that only statistical statements can be made about the outcome of measurements. For the interference experiment considered in this lesson, this means: one cannot say in advance at which point on the screen the next photon will be detected. One can only state the probability with which it will be found at a particular location (cf. Lesson 4.2 “The double-slit experiment with individual photons and the probabilistic statements of quantum theory”).