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My understanding was this:

In non-relativistic QM, the state of a system can be represented by the wavefunction, which can be written as a function of all the particles positions (well, and spins). The norm of the wavefunction is defined to be the probability density, and the wavefunction evolves according to the Schrodinger equation.

In Bohmian mechanics, there is also a wavefunction (pilot wave) which evolves according to the Schrodinger equation. ADDITIONALLY, there are particles which move according to the classical Hamiltonian with an additional "quantum potential" determined by the pilot wave.

__Please note:__I provided that information to give a 'snapshot' of my current level of understanding Bohmian mechanics and its contrasts with QM. What I wish is for someone to succinctly, and

*precisely*(with math) define and explain what Bohmian mechanics is.

In particular these things confuse me:

What are the "pilot waves" functions of for BM? (since the particles have a definite position and momentum, they can't be functions of that)

And while the particle evolution is effected by the pilot wave, how do the particles effect the pilot wave?

In fact, how do the particles effect anything? Do they effect the potential for other particles, or measurement (which means they would have to affect particles somehow), etc?