Related papers: Wigner function under changes of reference frames
A generalization of the classical electrodynamics for systems in absolute motion is presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate…
The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF…
This paper focus on the theoretical analysis and simulation of electromagnetic wave transforms, which is widely encountered in teaching physics. When the electromagnetic wave is not consistent with the shape of the object, it is often…
Using the notion, developed in an earlier paper, of "representation" of "position" by a vector in a vector space with an inner product, we show that the Lorentz Transformation Equations relating positions in two different reference frames…
In the literature on quantum reference frames, the internal (relative) properties of a system are defined as those which are preserved under an arbitrary change of reference frame. For a system of quantum spins, these are all properties…
We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the…
Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition…
Gauge-invariant Wigner theory describes the quantum-mechanical evolution of charged particles in the presence of an electromagnetic field in phase space, which is spanned by position and kinetic momentum. This approach is independent of the…
We consider some of the methods that can be used to reveal the general features of how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical…
We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion coefficients addressed in the literature are…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
The equation of the Doppler shift of two bodies in inertial motion in a reference frame at rest (i.e., stationary reference frame) is derived. In this derivation, the wave-particle duality of photons in the theory of special relativity is…
Previously, an explicit solution for the time evolution of the Wigner function was presented in terms of auxiliary phase space coordinates which obey simple equations that are analogous with, but not identical to, the classical equations of…
It is shown that a general model for particle detection in combination with a linear application of the Wigner rotations, which correspond to momentum-dependent changes of the particle spin under Lorentz transformations, to the state of a…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
Let $V_\Gamma$ be a lattice periodic potential and $A$ and $\phi$ external electromagnetic potentials which vary slowly on the scale set by the lattice spacing. It is shown that the Wigner function of a solution of the Schroedinger equation…