Related papers: The Snell law for quaternionic potentials
The motion of a magnetic spin particle in electromagnetic fields is considered on the basis of general principles of the classical relativistic theory. Alternative approaches in derivation of the equations of charge motion and spin…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
We show an example of benign non-separability in an apparently separable system consisting of $n$ free non-correlated quantum particles, solitonic solutions to the nonlinear phase modification of the Schr\"{o}dinger equation proposed…
We derive a new kinetic and a porous medium equations from the nonlinear Schr\"odinger equation with random potentials. The kinetic equation has a very similar form with the 4-wave turbulence kinetic equation in the wave turbulence theory.…
We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing)…
It is shown that the quaternionic Hilbert space formulation of quantum mechanics allows a quantization, based on a generalized system of imprimitivity, that leads to a description of the motion of a quantum particle in the field of a…
This article examines the consequences of the existence of an upper particle momentum limit in quantum electrodynamics, where this momentum limit is the Planck momentum. The method used is Fourier analysis as developed already by Fermi in…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
A relation between classical electrostatic fields and Schr\"odinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the…
General features of nonlinear quantum mechanics are discussed in the context of applications to two-level atoms.
Forces parallel to particle trajectories occur in physically meaningful situations, including relativistic cosmology and Einstein frame scalar-tensor gravity. These situations have Newtonian analogues that we discuss to provide intuition…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…