BogolyubovLogunovTodorov by Bohlin T.

By Bohlin T.

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As mentioned above, de Broglie stated that the quantum potential is related to the second derivative of the amplitude of the wave function ip = Re'e. Bohm, who proposed the theory of localized hidden variables in 1952, derived this quantum potential. It is independent of the phase, 6, of the wave function, and is represented in the form of V = h2V2R/2mR, where R is the amplitude of the wave, m is the mass of the particle, and h the Planck constant. With such a quantum potential, 20 Quantum Mechanics in Nonlinear Systems Bohm believed that the motions of microscopic particles should follow the Newton's equation, and it is because of the "instantaneous" action of this quantum potential, a measurement process is always disturbed.

Motivated by this thought, Bohm put forward the first systematic "hidden variable theory" in 1952. He believed that the statistical characteristics of linear quantum mechanics is due to some "background" fluctuations hidden behind the quantum theory. If we can find the hidden function for a microscopic particle, then a deterministic description could be made for a single particle. But how can the existence of such hidden variables be proved? Bohm proposed two experiments, to measure the spin correlation of a single proton and the polarization correlation in annihilating radiation of photons, respectively.

A magnetic field higher than 9 — 11 T is normally required. At present, atomic hydrogens cannot be compressed to the density of 1019 cm" 3 . The methods for avoiding recombination of atomic hydrogens are thus limited. It has not been possible to directly observe the condensation of spin polarized hydrogen atoms and the associated macroscopic quantmn effects. 3 Bose-Einstein condensation of excitons It is well known that an electron and a hole can form a bound state, or an exciton, due to the Coulomb interaction between them in many materials such as silicon, germanium, cadmium sulphide, arsenical bromine, silicon carbide, etc..

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