Bohm's quantum potential as an internal energy

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.