Related papers: Local quantum mechanics with finite Planck mass
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.…
Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…
The problem of quantum gravity is treated from a radically new viewpoint based on a detailed mathematical analysis of what the constitution of physical space is, which has been carried out by Michel Bounias and the author. The approach…
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…
We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription in…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
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…
We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int…
A two-dimensional quantum mechanical system consisting of a particle coupled to two magnetic impurities of different strengths, in a harmonic potential, is considered. Topological boundary conditions at impurity locations imply that the…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum,…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
The motion of a classical spinning test particle in the field of a weak plane gravitational wave is studied. It is found that the characteristic dimensions of the particle's orbit is sensitive to the ratio of the spin to the mass of the…
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 amplitude, Born rule,…
For the purpose of analyzing observed phenomena, it has been convenient, and thus far sufficient, to regard gravity as subject to the deterministic principles of classical physics, with the gravitational field obeying Newton's law or…