In this note, we consider the mathematical aspects of functional mechanics proposed and developed by I. V. Volovich. particular, briefly review Liouville equation used to describe dynamics wave packets, study characteristics such as their averages dispersions, features in case Hamiltonian Lagrangian theory, give a number simple examples illustrating general constructions.

We constructed a method of phase unwrapping for a typical wave-front by utilizing the maximizer of the posterior marginal (MPM) estimate corresponding to equilibrium statistical mechanics of the three-state Ising model on a square lattice on the basis of an analogy between statistical mechanics and Bayesian inference. We investigated the static properties of an MPM estimate from a phase diagram...

In this paper a one to one correspondence is established between spacetime metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and from there, passing directly to a corresponding expression in the dual space. It is shown that in the case of a massless particle, Maxwell’s equation for a phot...

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under...

A means for separating subjective and objective aspects of the electron wave function is suggested, based on a reformulation of the Dirac Theory in terms of Spacetime Algebra. The reformulation admits a separation of the Dirac wave function into a two parameter probability factor and a six parameter kinematical factor. The complex valuedness of the wave function as well as its bilinearity in ob...

It is revisited the Michelson-Morley experiment within the quantum mechanics framework. One can define the wave function of photon in the whole space at a given moment of time. The phase difference between the source and receiver is a distance between the source and receiver at the time of reception hence it does not depend on the velocity of the frame. Then one can explain the null result of t...

A discussion of wave-particle duality can be found in all modern textbooks dealing with theories of chemical structure and bonding (I). Almost all of these contain some summary of the experimental evidence in favor of such duality, which comes from studies of the physics of electromagnetic radiation (ohotons vs. waves) and "elementarv" oarticles ,. . such as electrons, protons, neutrons, etc. U...

In this paper, I introduce an intrinsic account of the universal wave function. My account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is free from the usual arbitrary conventions in the wave function representation, and (3) it explains why the wave function has its ampl...

We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quanti-zation a consistent relativistic quantum mechanics, which reproduces literally the behavior of the one-particle sector of the corresponding quantum field. At the s...