Bohm's quantum potential as an internal energy

Highlights: • The quantum potential is seen as internal energy associated with a phase space region. • Fermi's trick shows that Bohm's particle is an extended structure in phase space. • We associate Bohm's quantum potential with a context-dependent energy redistribution. • A physically motivated derivation of Schrodinger's equation is provided. • We show the Fermi set associated with a 3-D coherent state contains a quantum blob. - Abstract: We pursue our discussion of Fermi's surface initiated by Dennis, de Gosson and Hiley and show that Bohm's quantum potential can be viewed as an internal energy of a quantum system, giving further insight into its role in stationary states. This implies that the 'particle' referred to in Bohm's theory is not a classical point-like object but rather has an extended structure in phase space which can be linked to the notion of a symplectic capacity, a topological feature of the underlying symplectic geometry. This structure provides us with a new, physically motivated derivation of Schrödinger's equation provided we interpret Gleason's theorem as a derivation of the Born rule from fundamental assumptions about quantum probabilities