What Can Quantum Mechanics Predict?

The previous post recalled the fact that standard Quantum Mechanics QM based on a $3N$ spatial dimensional Schrödinger equation for a system with $N$ electrons is effectively uncomputable for almost all atoms in the periodic table. With a resolution of $10^2$ in each spatial dimension, the total number of mesh points is daunting $10^{6N}$ which fills any thinkable computer already for $N=5$ (Boron). The wave function for all atoms beyond Boron is thus uncomputable. This means that the wave function for almost all atoms in the period table is uncomputable!

We compare with the standard message by physicists that all predictions of QM perfectly match with observation, or more precisely that there are no observations which contradict QM. 

The crucial question is then what predictions QM offers? Does QM predict the periodic table? A physicist would say that certainly this is so, in principle, while precise computations are lacking, because the full wave function is uncomputable. 

What can be computed are various low-dimensional approximations based on a variety of ad hoc assumptions. If such an ad hoc approximate solution happens to match observation, it is accepted as a demonstration that the full wave function (although unknown) also matches observation. If the ad hoc solutions does not match observation, it is discarded. With this strategy it is impossible to find a contradiction between theory and experiment! Success story!

But there is a caveat. Do you see it? Compare with How far does quantum mechanics explain the periodic table?

Real Quantum Mechanics presents a new Schrödinger equation as a non-linear system of non-overlapping electron charge densities sharing a common 3d space, thus a classical continuum model, which is computable for many electrons. A laptop computation for H2O is reported here with more to come.

Summary: QM in fact predicts very little (ab initio without ad hoc assumptions), which is consistent with the fact that there is no observation in contradiction with a QM prediction. But a theory which predicts nothing is not falsifiable and as such not a scientific theory. This is the reason behind the crisis of modern physics based on QM witnessed by so many physicists. Real QM opens a door out of the crisis. Why not give it a try? Permanent QM crisis over 100 years is not healthy to physics.