Did you read the link that you posted Jan?
Their method might be an interesting superset of classical and quantum methods but it is *extremely* mathematical and intricate mathematics. The standard QM formalism is way easier to use and understand.
That paper starts at the WKB approximation (which was part II theoretical physics back in my day and would be graduate level now) and goes off at at skyward tangent. It might indeed yield something by way of an insight into QM but it will still contain all known QM results as a limiting case. QM is experimentally validated to a high degree...
My money is on Clifford algebras to be the next big leap forward in physics notation that provides more insight (rather than string theory) but it has been a long coming. I know some folk in both camps.