Fermi's ansatz and Bohm's quantum potential

In this paper we address the following simple question: Given a wavefunction ψ(x,t) in a one-dimensional configuration space, is it possible to give a unique two-dimensional representation ρ(x,p,t) in a position-momentum phase plane? If so, can we find the general condition that makes this possible? We will show that this is indeed possible by using an idea introduced originally by Fermi provided the boundary of the phase space area is a closed curve satisfying a certain exact quantum condition. •We review “Fermi's trick” which allows one to view an arbitrary wavefunction as a stationary state for some Hamiltonian operator HF. This Hamiltonian contains the quantum potential.•We study the relation between Fermi's trick and an exact quantization condition which reduces to the familiar EBK condition in the limit ħ→0.•This allows us to relate the Fermi set HF(x,p)=0 to the notion of quantum blob introduced by one of us in previous work. Quantum blobs are phase space regions corresponding to minimum uncertainty.•We discuss our results from the point of view of the quantum theory of motion.