Related papers: Delay Time in Quaternionic Quantum Mechanics
The paper reviews positive and negative time delays in various processes of classical and quantum physics. In the beginning, we demonstrate how a time-shifted response of a system to an external perturbation appears in classical mechanics…
In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential…
We compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. This analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be…
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
We revisit the formulation of quantum mechanics over the quaternions and investigate the dynamical structure within this framework. Similar to standard complex quantum mechanics, time evolution is then mediated by a unitary operator which…
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a…
In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The…
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…
The concept and the formalization of the arrival time in quantum mechanics are discussed. Different approaches based on trajectories, quantization rules, time operators, phase space techniques, renewal equations or operational procedures…
Solutions of quaternionic quantum mechanics (QQM) are difficult to grasp, even in simple physical situations. In this article, we provide simple and understandable free particle quaternionic solutions, that can be easily compared to complex…
We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal…
The unavoidable finite time intervals between the sequential operations needed for performing practical quantum computing can degrade the performance of quantum computers. During these delays, unwanted relative dynamical phases are produced…
Among the many perplexing results of quantum mechanics is one that contradicts a result from introductory physics: the possibility of finding a quantum particle in a region that would be forbidden classically by energy conservation. An…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
We derive the time dilation formula for charged quantum clocks in electromagnetic fields. As a concrete example of non-inertial motion, we consider a cyclotron motion in a uniform magnetic field. Applying the time dilation formula to…