Related papers: Quaternionic Quantum Mechanics: the Particles, the…
It is demonstrated how quantum mechanics emerges from the stochastic dynamics of force-carriers. It is shown that the quantum Moyal equation corresponds to some dynamic correlations between the momentum of a real particle and the position…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
In view of experimentally obtainable resolutions, equal to the Compton wavelength of an electron, the conventional interpretation of quantum mechanics no longer seems to provide a sufficiently subtle tool. Based on the intrinsic properties…
Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present work, we suggest such a derivation in…
Suppose the usual description of spacetime as a 4-dimensional manifold with a Lorentzian metric breaks down at Planck energies. Can we still construct sensible theoretical models of the universe? Are they testable? Do they lead to a…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the electrodynamic force law, the Poynting vector, the energy…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
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…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
Fundamental solutions for the free Dirac electron and Einstein photon equations in position coordinates are constructed as matrix valued functionals on the space of bump functions. It is shown that these fundamental solutions are related by…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
In the process of work it has been found that space-time quantum fluctuations are naturally described in terms of the deformation parameter introduced on going from the well-known quantum mechanics to that at Planck scales and put forward…
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex…
Quantum Mechanics at Planck scale is considered as a deformation of the conventional Quantum Mechanics. Similar to the earlier works of the author, the main object of deformation is the density matrix. On this basis a notion of the entropy…
We study the bound-state solutions of vanishing angular momentum in a quaternionic spherical square-well potential of finite depth. As in the standard quantum mechanics, such solutions occur for discrete values of energies. At first glance,…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed…
By using the analogy between optics and quantum mechanics, we obtain the Snell law for the planar motion of quantum particles in the presence of quaternionic potentials.