Related papers: Can a particle moves zigzag in time?
A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude…
We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system…
The delay time associated with a scattering process is one of the most important dynamical aspects in quantum mechanics. A common measure of this is the Wigner delay time based on the group velocity description of a wave-packet, which my…
The propagation of a localized wave packet in the conical space-time created by a pointlike massive source in 2+1 dimensional gravity is analyzed. The scattering amplitude is determined and shown to be finite along the classical scattering…
We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and…
Time crystals, a unique non-equilibrium quantum phenomenon with promising applications in current quantum technologies, mark a significant advance in quantum mechanics. Although traditionally studied in atom-cavity and optical lattice…
We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite…
In this article, spatially-structured gravitational waves are investigated. Drawing upon analogies between electrodynamics and general relativity, a new gauge is found. We investigate the polarization and degrees of freedom of the resulting…
Under broad conditions, we prove that the probability amplitudes in the quantum mechanics are either always constant in time or changing continuously in any interval of time.
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic…
Although the standard viewpoint in theoretical physics is that the unification of quantum theory and general relativity requires the quantization of gravity and spacetime, there is not consensus about whether spacetime must fundamentally…
The aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in quantum mechanics and also partially in…
Kappa-Minkowski space-time is an example of noncommutative space-time with potentially interesting phenomenology. However, the construction of field theories on this space is plagued with ambiguities. We propose to resolve certain…
The perspective is advanced that the time parameter in quantum mechanics corresponds to the time coordinate in a Minkowski flat spacetime local approximation to the actual dynamical curved spacetime of General Relativity, rather than to an…
Rapidly oscillating potentials with a vanishing time average have been used for a long time to trap charged particles in source-free regions. It has been argued that the motion of a particle in such a potential can be approximately…
In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short…
We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…