The amplitude-dependent extra potential in the Madelung equations. Taking the gradient of their phase equation and using the guidance equation yields , where is the material derivative. At wavefunction nodes this local expression may be singular.
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Quantum potential is a concept from quantum mechanics that arises in the context of de Broglie-Bohm theory, also known as pilot-wave theory. In this interpretation of quantum mechanics, particles have definite trajectories guided by a "pilot wave," which is described by the wave function. The quantum potential influences the motion of particles and is derived from the wave function of the system.