De Broglie–Bohm guidance equations for arbitrary Hamiltonians

Abstract

In a pilot-wave theory, an individual closed system is described by a wavefunction ψ(q) and configuration q. The evolution of the wavefunction and configuration are respectively determined by the Schrödinger and guidance equations. The guidance equation states that the velocity field for the configuration is given by the quantum current divided by the density |ψ(q)|2. We present the currents and associated guidance equations for any Hamiltonian given by a differential operator. These are derived directly from the Schrödinger equation, and also as Noether currents arising from a global phase symmetry associated with the wavefunction in configuration space.