Related papers: Probability density of relativistic spinless parti…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schr\"odinger equation.…
A simple relativistic quantum hidden-variable theory of particle trajectories, similar to the Bohm theory but without nonlocal forces between the particles, is proposed. To provide compatibility with statistical predictions of quantum…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories…
The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis and calculation of the reflection and transmission coefficients for the scattering of particles in a…
Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic…
The existence of precise particle trajectories in any quantum state is accounted for in a consistent way by allowing delocalization of the particle charge. The relativistic mass of the particle remains within a small volume surrounding a…
It is shown that the alternative Klein-Gordon equation with positive definite probability density proposed in a letter by M.D. Kostin does not meet the requirements of relativistic (quantum) field theory and therefore does not allow for a…
We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Metrics are considered…
In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a time $T$, that we take very large, when this extreme…
Imposing the Born rule as a fundamental principle of quantum mechanics would require the existence of normalizable wave functions also for relativistic particles. Indeed, the Fourier transforms of normalized k-space amplitudes yield…
Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
We derive $q$-versions of Green's theorem from the Leibniz rules of partial derivatives for the $q$-deformed Euclidean space. Using these results and the Schr\"{o}dinger equations for a $q$-deformed nonrelativistic particle, we derive…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
We provide a proof that the stationary macroscopic current of particles in a random lattice Lorentz gas satisfies Fick's law when connected to particles reservoirs. We consider a box on a d+1 dimensional lattice and when $d\geq7$, we show…
The probability density of a quantum particle moving freely within a circular ring can exhibit local flow patterns inconsistent with its angular momentum, a phenomenon known as quantum backflow. In this study, we examine a quantum particle…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…