Pilot wave

In the laboratory frame this electromagnetic field configuration has the total energy hv = me2. Thereby the fraction (m — mo)c2 can be regarded as the energy of a free pilot wave of radiation, and the fraction moc2 as the energy... 

Bohm s failure to give an adequate explanation to support the pilot-wave proposal does not diminish the importance of the quantum-potential concept. In all forms of quantum theory it is the appearance of Planck s constant that signals non-classical behaviour, hence the common, but physically meaningless, proposition that the classical/quantum limit appears as h —> 0. The actual limiting condition is Vq —> 0, which turns the quantum-mechanical... 

Broglie s idea [32] of a pilot wave were later developed by Bohm [4] into an ontic interpretation1 of quantum mechanics. 

In terms of the quantum-potential formulation particle trajectories can be associated with the quantum HJ equation (6) in exactly the same way as in the classical case [34, 35]. As before, particle trajectories associated with the phase S may be obtained by constructing the normals to S, each one distinguished by its initial coordinates. By this procedure Bohm managed to revive the pilot-wave model of De Broglie. It means that a point particle of mass m on a trajectory x = x(t), is now associated with the physical... 

Elucidation of the non-local holistic nature of quantum theory, first discerned by Einstein [3] and interpreted as a defect of the theory, is probably the most important feature of Bohm s interpretation. Two other major innovations that flow from the Bohm interpretation are a definition of particle trajectories directed by a pilot wave and the physical picture of a stationary state. 

The beat pattern consists of what is known as a pilot wave or a wave packet. As indicated in the diagram, one of the ways to localize the wave packet into a narrow region of space is to combine two waves that have vastly different wavenumbers (the wavenumber I /A is directly related to the momentum by a factor of h). Thus, in order to minimize the uncertainty in the position, a wider range of wavelengths (or a greater uncertainty in momentum) is required, as illustrated in Figure 3.22. This is simply a qualitative restatement of the Heisenberg uncertainty principle. 

In the mind of de Broglie, the wave accompanies the particle. He also talked about a pilot wave that guided the particle in its path. It is unclear in the theory of de Broglie what the physical meaning of the matter wave is. Is it a longitudinal wave like sound waves How then could waves appear in a vacuum The meaning of the waves was not cleared up until the interpretation of Max Born some years later. 

In 1952, David Bohm (following a suggestion made by de Broglie in 1927 that the wave function might act as a pilot wave guiding the motion of the particle) devised a nonlocal deterministic hidden-variable theory that predicts the same experimental results as quantum mechanics [D. Bohm, Phys. Rev., 85, 166, 180 (1952)]. In Bohm s theory, a... 

In 1923, De Broglie proposed the seemingly strange concept that there is some sort of mathematical pilot wave that can be used to describe the behavior of particles as given by... 

We will now present a derivation of the Schrodinger equation that may not be the way he thought of it but that follows from limited use of calculus and simple algebra. Since De Broglie implied there is some sort of invisible, untouchable, mathematical pilot wave accompanying the motion of particles, we assume the general form of such a wave and relate it to its own second derivative. We will use i j since it is universally used for the wave function. 

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