= Solution
<Bohmian mechanics> retains definite particle positions and deterministic trajectories, which makes it resemble <classical mechanics> at one level. But the guiding dynamics depends on a <wavefunction> obeying the <Schrödinger equation>, with <velocity> schematically $\dot Q_i=(\hbar/m_i)\operatorname{Im}(\nabla_i\psi/\psi)(Q)$. For many particles this <wavefunction> is defined on <configuration space> and can be entangled. The <velocity> of one particle can consequently depend on the configuration of distant particles. Classical-looking trajectories therefore do not entail classical locality or separability.
Writing $\psi=R e^{iS/\hbar}$ also yields a Hamilton-Jacobi-like equation with <quantum potential> $Q=-\sum_i\hbar^2\nabla_i^2R/(2m_iR)$. The <quantum potential> is not generally a sum of ordinary <Pair potential>[pair potentials] in three-space; its configuration dependence carries the nonclassical correlations. A stationary real bound-state <wavefunction> can give a stationary particle configuration, unlike the <orbit (dynamical system)>[orbit] one might infer from a classical Coulomb picture. Measurement outcomes are contextual: the actual apparatus interaction helps determine which position record is produced.
With the quantum-equilibrium distribution $\rho=|\psi|^2$, the guidance and <Wave equation>[wave equations] preserve that distribution and reproduce the usual <quantum statistics>. Determinism alone does not establish that distribution; <equilibrium> or typicality is an additional explanatory component. The theory also leaves philosophical choices about whether the <wavefunction> is a physical field, a law-like object or part of a broader ontology.
The significant departure is therefore not simply replacing chance by hidden classical motion. It is the entangled guiding structure, nonlocal dependence and contextual relation between measurements and properties. The retained particles make the account continuous with some classical intuitions, while its actual law and ontology depart substantially from classical many-body mechanics.<A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables I by David Bohm>[1952, guidance dynamics and quantum potential]{ref}<A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables II by David Bohm>[1952, measurement and statistical interpretation]{ref}
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