We must regard the Schrodinger equation not as showing that matter also behaves like a wave. That is so archaic that I want to throw up.

No. The Schrodinger equation was the first Quantum Field Theory. The mathematical "waves" it produces is merely a reflection of the mathematical tools we humans have available that can describe how physical processes are probabilistic and not uni-deterministic.

But this is nothing new. The probabilistic interpretation of the wave function is 100 years old, and it is about time to take the idea seriously.