Equivalence Postulate and the Quantum Potential of Two Free Particles

TL;DR

This paper explores how the Equivalence Postulate leads to the quantum Hamilton-Jacobi equation and shows that the quantum potential acts as an interaction term for two free particles, with implications for energy quantization and classical limits.

Contribution

It demonstrates that the cocycle condition from the EP uniquely derives the quantum Hamilton-Jacobi equation and interprets the quantum potential geometrically as an interaction term.

Findings

Quantum potential depends on constants with geometric meaning.

Energy quantization arises from local homeomorphicity.

Solutions exist that do not vanish in the classical limit.

Abstract

Commutativity of the diagram of the maps connecting three one--particle state, implied by the Equivalence Postulate (EP), gives a cocycle condition which unequivocally leads to the quantum Hamilton--Jacobi equation. Energy quantization is a direct consequences of the local homeomorphicity of the trivializing map. We review the EP and show that the quantum potential for two free particles, which depends on constants which may have a geometrical interpretation, plays the role of interaction term that admits solutions which do not vanish in the classical limit.