16 Facts About Quantum potential

The quantum potential approach introduced by Bohm provides a physically less fundamental exposition of the idea presented by Louis de Broglie: de Broglie had postulated in 1925 that the relativistic wave function defined on spacetime represents a pilot wave which guides a quantum particle, represented as an oscillating peak in the wave field, but he had subsequently abandoned his approach because he was unable to derive the guidance equation for the particle from a non-linear wave equation.

The seminal articles of Bohm in 1952 introduced the quantum potential and included answers to the objections which had been raised against the pilot wave theory.

Bohm quantum potential is closely linked with the results of other approaches, in particular relating to work by Erwin Madelung of 1927 and to work by Carl Friedrich von Weizsacker of 1935.

Quantum potential, expressed in terms of the probability density function, becomes:.

Quantum potential force, expressed in terms of the probability distribution, amounts to:.

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In line with David Bohm's approach, Basil Hiley and mathematician Maurice de Gosson showed that the quantum potential can be seen as a consequence of a projection of an underlying structure, more specifically of a non-commutative algebraic structure, onto a subspace such as ordinary space.

Giovanni Salesi, Erasmo Recami and co-workers showed in 1998 that, in agreement with the Konig's theorem, the quantum potential can be identified with the kinetic energy of the internal motion associated with the spin of a spin-½ particle observed in a center-of-mass frame.

The quantum potential plays the role of an internal energy which ensures the conservation of total energy.

Quantum potential approach was extended by Hiley and co-workers to quantum field theory in Minkowski spacetime and to curved spacetime.

Quantum force exerted by the relativistic quantum potential is shown to depend on the Weyl gauge potential and its derivatives.

Quantum potential emphasized however that to give the Klein–Gordon theory a single-particle interpretation in terms of trajectories, as can be done for nonrelativistic Schrodinger quantum mechanics, would lead to unacceptable inconsistencies.

Quantum potential developed a generalized relativistic-invariant probabilistic interpretation of quantum theory, in which is no longer a probability density in space but a probability density in space-time.

Basil Hiley showed that the energy–momentum-relations in the Bohm model can be obtained directly from the energy–momentum tensor of quantum field theory and that the quantum potential is an energy term that is required for local energy–momentum conservation.

Quantum potential has hinted that for particle with energies equal to or higher than the pair creation threshold, Bohm's model constitutes a many-particle theory that describes pair creation and annihilation processes.

The quantum potential is referred to in association with Bohm's name as Bohm potential, quantum Bohm potential or Bohm quantum potential.

Approach using Bohmian trajectories and the quantum potential is used for calculating properties of quantum systems which cannot be solved exactly, which are often approximated using semi-classical approaches.