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Mark P. Davidson

Publications and source records attributed to Mark P. Davidson.

12 recordsLinked to original sources
arXiv2019

Comments on the nonlinear Schrodinger equation

A proof is given that if the nonlinear Schrodinger wave function is constrained to have support over only a finite volume in configuration space, then the total energy is bounded from below for either sign of the logarithmic term in the Hamiltonian. It is concluded that the usual assumption about the sign of the logarithmic term made by Bialynicki-Birula and Mycielski is not the only possibility, and that a sensible theory can be made with the opposite sign as well.

quant-ph↗
arXiv2006

Stochastic Models of Quantum Mechanics - A Perspective

A subjective survey of stochastic models of quantum mechanics is given along with a discussion of some key radiative processes, the clues they offer, and the difficulties they pose for this program. An electromagnetic basis for deriving quantum mechanics is advocated, and various possibilities are considered. It is argued that only non-local or non-causal theories are likely to be a successful basis for such a derivation.

quant-ph↗
arXiv2006

Quantum wave equations and non-radiating electromagnetic sources

A connection between classical non-radiating sources and free-particle wave equations in quantum mechanics is rigorously made. It is proven that free-particle wave equations for all spins have currents which can be defined which are non-radiating electromagnetic sources. It is also proven that the advanced and retarded fields are exactly equal for these sources. Implications of these results are discussed.

quant-ph↗
arXiv2006

An analysis of semiclassical radiation from single particle quantum currents shows surprising results

Classical electromagnetic radiation from quantum currents and densities are calculated. For the free Schrodinger equation with no external force it's found that the classical radiation is zero to all orders of the multipole expansion. This is true of mixed or pure states for the charged particle. It is a non-trivial and surprising result. A similar result is found for the Klein-Gordon currents when the wave function consists of only positive energy solutions. For the Dirac equation it is found that radiation is suppressed at lower frequencies but is not zero at all frequencies. Implications of these results for the interpretation of quantum mechanics are discussed.

quant-ph↗
arXiv2006

Predictions of the hydrodynamic interpretation of quantum mechanics compared with quantum electrodynamics for low energy bremsstrahlung

It is shown that the hydrodynamic interpretation of a charged quantum particle leads to a different theoretical prediction for low energy bremsstrahlung than does quantum electrodynamics (QED). In the calculations, the electromagnetic fields are treated classically in the hydrodynamic case, but are quantized in QED. Calculations show the hydrodynamic model to have a different and more sensitive dependence on the size and shape of the radiating particle's wave packet then does QED. In particular it is shown that bremsstrahlung is sometimes greatly reduced when the force acting on the particle is localized to a volume small compared to the particle's wave packet. QED exhibits no such reduction. Therefore it is possible to test this effect experimentally. An experiment is proposed. It involves an electron microscope with a Wien filter for producing monochromatic beam electrons and an accurate energy measurement of the particle after passing through a local force field.

quant-ph↗
arXiv2004

Bremsstrahlung from Charged Bose-Einstein Condensates

Low energy bremsstrahlung formulae are derived for a particle beam of charged bosons forming a Bose-Einsten condensate. The expression for energy radiated consists of two terms in this case. One of them, the larger one in the limit of large numbers of Bosons in the state, is proportional to the number of bosons squared and has the same form as one obtains in a hydrodynamic model of quantum wave mechanics. This term is sensitive to the size and shape of the wave packet especially when the force field causing acceleration is localized in extent. The second term, identical to the single particle scattering formula, is less sensitive to the wave packet size and shape and is proportional to the number of bosons in the condensate. The conclusion is that for a Bose-Einstein condensate the radiated bremsstrahlung is a sensitive function of the wave packet shape which is quite different than for a beam of incoherent particles which do not show very much dependence on the wave packet. Only lowest order radiation is calculated. It is also found that to lowest order there does not exist any situation in which the radiation loss from a coherent state of bosons vanishes completely, so that there is no analog of superconductivity in a particle beam of this type at least within the net of assumptions made in this paper. The amount of radiation can be greatly suppressed however, as it is a sensitive function of the form of the wave function.

quant-ph↗
arXiv2002

A modal model for diffraction gratings

A description of an algorithm for a rather general modal grating calculation is presented. Arbitrary profiles, depth, and permittivity are allowed. Gratings built up from sub-gratings are allowed, as are coatings on the sidewalls of lines, and arbitrary complex structure. Conical angles and good conductors are supported.

physics.optics↗
arXiv2001

A model for the stochastic origins of Schrodinger's equation

A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrodinger's equation as a solution. It suggests that the origins of the peculiar and nonclassical features of quantum mechanics are actually inherent in a statistical description of the radiative reactive force.

quant-ph↗
arXiv2001

Momentum in stochastic quantum mechanics

Momentum is analyzed as a random variable in stochastic quantum mechanics. Arbitrary potential energy functions are considered. The oscillator is presented as an example.

quant-ph↗
arXiv2001

The origin of the algebra of quantum operators in the stochastic formulation of quantum mechanics

The origin of the algebra of the non-commuting operators of quantum mechanics is explained in the general Fenyes-Nelson stochastic models in which the diffusion constant is a free parameter. This is achieved by continuing the diffusion constant to imaginary values, a continuation which destroys the physical interpretation, but does not affect experimental predictions. This continuation leads to great mathematical simplification in the stochastic theory, and to an understanding of the entire mathematical formalism of quantum mechanics. It is more than a formal construction because the diffusion parameter is not an observable in these theories.

quant-ph↗
arXiv2001

A generalization of the Fenyes-Nelson stochastic model of quantum mechanics

It is shown that the stochastic model of Fenyes and Nelson can be generalized in such a way that the diffusion constant of the Markov theory becomes a free parameter. This extra freedom allows one to identify quantum mechanics with a class of Markov processes with diffusion constants varying from zero to infinity.

quant-ph↗