Quantum potential

The quantum potential is a term in Bohmian mechanics derived from the curvature of a wavefunction’s amplitude. It enters the guidance dynamics alongside the classical potential and can shape particle trajectories.

Bohmian mechanics: An interpretation of quantum mechanics in which particles have definite positions guided by a wavefunction. The quantum potential is one ingredient in this theory’s account of particle motion.
Wavefunction: A complex-valued function encoding a quantum system’s state and the probabilities of measurement outcomes. Its amplitude supplies the function whose curvature defines the quantum potential.
Classical potential energy: Position-dependent energy that determines forces in classical mechanics. It enters Bohmian dynamics alongside the quantum potential but has a classical source.
Double-slit experiment: An experiment in which particles or waves pass through two openings to produce an interference pattern. Its interference structure creates spatial amplitude variations that shape Bohmian paths.
Ontology of Bohmian mechanics: The question of what entities Bohmian mechanics treats as physically real. Whether the quantum potential is a physical influence or mathematical description depends on this broader issue.
Madelung transformation: A decomposition of a complex wavefunction into an amplitude and a phase. Separating amplitude from phase exposes the term that becomes the quantum potential.
Probability amplitude: A complex number whose squared magnitude contributes to the probability of a quantum outcome. The quantum potential depends on the spatial variation of the wavefunction’s amplitude.
Quantum force: The force-like term obtained from the negative gradient of the quantum potential. The force is a gradient-derived effect, not the potential itself.
Gaussian wave packet: A wave packet whose spatial amplitude has a Gaussian profile. Its calculable curvature makes it a standard example for evaluating the quantum potential.
Nonlocality: Dependence between spatially separated systems that cannot be explained by local influences alone. For entangled states, the quantum potential can depend on the configuration of distant particles.

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