Related papers: Quantum mechanics: A new chapter?
Based on an observation that the basic mode of a common microwave waveguide is a solution to the Klein-Gordon equation, quantum mechanics is modeled as the wave-function propagated inside a waveguide. The guide width is determined by the…
Recent experiments involving semiconducting quantum dots embedded in Aharonov-Bohm interferometry setups suggest that information concerning the phase of electron wavefunctions can be obtained from transport measurements. Here we review the…
We generalize the formerly proposed relationship between a special complex geometry (originating from the structure of biquaternion algebra) and induced real geometry of (extended) space-time. The primordial dynamics in complex space allows…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
In this paper, we demonstrate novel relationships between quantum mechanics and the electromagnetic wave equation. In our approach, an invariant interference-dependent electromagnetic quantity, which we call "quantum rest mass", replaces…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…
The issue of non-locality in quantum mechanics can potentially be resolved by considering relativistically covariant diffusion in four-dimensional spacetime. Stochastic particles described by the Klein-Gordon equation are shown to undergo a…
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum…
Although electrons and photons produce the same interference patterns in the two-slit experiments, the description of these patters is markedly different. This difference was analyzed by Bohm. Later on Sanz and Miret-Artes and others were…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
We propose that the mechanism responsible for the ``collapse of the wave function" (or "decoherence" in its broadest meaning) in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike…
An ab initio, three-dimensional quantum mechanical calculation has been performed for the time-evolution of continuum electrons in the fields of moving charges. Here the essential singularity associated with the diverging phase factor in…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…