Old quantum postulate was E= h w, where w= 2 pi/ t.
Nowadays, we depart from the (afaik) equivalent postulate [x,p]=ih. I suposse this was originated by Dirac methodology.

Which are the merits and disadvantages of each postulate? For instance, the old one seems more physical, but I have never seen a quantum field theory formulated from the old principle. Also, it is very intriguing to see how to fit both postulates into the path integral formulation.

Originally posted by arivero
Old quantum postulate was E= h w, where w= 2 pi/ t.
Nowadays, we depart from the (afaik) equivalent postulate [x,p]=ih. I suposse this was originated by Dirac methodology.

Which are the merits and disadvantages of each postulate? For instance, the old one seems more physical, but I have never seen a quantum field theory formulated from the old principle. Also, it is very intriguing to see how to fit both postulates into the path integral formulation.

there are several ways to quantize a system. one is to assume that x -> X (operator), and p-> hbar/i d/dx, and substitute those into your classical hamiltonian. this gives you schroedinger s wave mechanics. another is to assume [x,p]=hbar*i. one of the advantages of this is that it is coordinate independent, so can be used in more general systems. for the right choice of coordinates, the two approaches are equivalent.

E=hw was a hypothesis based on experiment. this is never used as a starting point for any quantum system, as it is not, in general, true.

the path integral formulation is another different approach.