# On particle diffraction and its relation to the statistical interpretation of the wave function

Particles can be diffracted due to their quantum nature and that is understood by their wave-like behavior. Clearly seen in e.g. plane wave solutions of the Schrodinger equation or a superposition of states which can be seen as a wave packet.

Statistical interpretation tells that those wave functions are merely to describe probability amplitudes, so one can argue they are not ontic/ physical waves.

On the basis of these two statements, why/how can de Broglie wavelength be used as in the classical wave approach to determine if a quantum object will be diffracted by a slit, lattice, nucleus etc. ?

In a section of Heisenberg's The Physical Principles of Quantum Theory; he emphasizes Duane's perspective on corpuscular picture of diffraction/reflection and points out for example for a grating, if it is known that the particle will hit a certain $$\Delta x$$ of the grating then the momentum will become uncertain by an amount proportional to $$\frac{h}{\Delta x}$$ The reflection direction will therefore be uncertain according to the relation above. The value of this uncertainty can be calculated from the resolving power of a grating of
$$\frac{\Delta x}{d}$$ lines; d being a plane ruled grating's constant. When, $$\Delta x < < d$$ the interference maxima are no longer visible and the trajectory can be compared to that of a classical particle.