Related papers: Transformation of a wavefunction under changes of …
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…
Quantum groups have been widely explored as a tool to encode possible nontrivial generalisations of reference frame transformations, relevant in quantum gravity. In quantum information, it was found that the reference frames can be…
We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal…
We introduce the Hamiltonian dynamics with the Hartree-Fock energy in new {\it wave-matrix} picture. Roughly speaking, the wave matrix is defined as the square root of the density matrix. The corresponding Hamiltonian equations are…
Single-photon transitions are one of the key technologies for designing and operating very-long-baseline atom interferometers tailored for terrestrial gravitational-wave and dark-matter detection. Since such setups aim at the detection of…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.
We introduce and study a new integral ray transform called the head wave transform. The head wave transform integrates a function along a piecewise linear (in general geodesic) path consisting of three parts. The geometry of such paths…
The Madelung transformation of the space in which a quantum wave function takes its values is generalized from complex numbers to include field spaces that contain orbits of groups that are diffeomorphic to spheres. The general form for the…
We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with repsect to a…
Data augmentation in feature space is effective to increase data diversity. Previous methods assume that different classes have the same covariance in their feature distributions. Thus, feature transform between different classes is…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
The use of image transformations is essential for efficient modeling and learning of visual data. But the class of relevant transformations is large: affine transformations, projective transformations, elastic deformations, ... the list…
We analyze the issue of the interpretation of the wavefunction, namely whether it should be interpreted as describing individual systems or ensembles of identically prepared systems. We propose an experiment which can decide the issue,…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
In this note we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
Light scattering is the main limitation for optical imaging. However, light can be focused through or inside turbid media by spatially shaping the incident wavefront. Wavefront shaping is ultimately limited by the available photon budget.…