QM most certainly does account for and predict an enormous range of observed behaviours of the world.
Have you ever come across the Periodic Table? Do you know why it is laid out the way it is?
Have you ever seen a line spectrum? Do you now why the lines appear where they do?
None of these behaviours i actually proven, when you actually see those experiments, and see how they conduct experiments, the fact is you cannot see anything what is proven.
They simply repeat what models say, but they ignore what exactly experiments show, indicate or prove.