Related papers: Transformation of a wavefunction under changes of …
We consider propagation of high-frequency wave packets along a smooth evolving background flow whose evolution is described by a simple-wave type of solutions of hydrodynamic equations. In geometrical optics approximation, the motion of the…
For a non-relativistic particle subject to a Hamiltonian that is quadratic in position and momentum, with coefficients that may vary with time, it is shown that the effect of the linear terms in the Hamiltonian is just a spatial translation…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
We show that the transformation equation for the tardyon velocity involves two generic functions which in turn depend on the relative velocity of the involved reference frames, on the tardyon velocity u and on the polar angle which define…
A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications follow. Related compatibility questions for…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of…
Using Pathak and Pathak techniques, the basic function $D^\alpha(u,v,w)$ associated with general novel fractional wavelet transform (GNFrWT)is defined and its properties are investigated. By using basic function $D^\alpha(u,v,w)$…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
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…
The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays.…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
The main result of this note is a characterization of the Poisson commutativity of Hamilton functions in terms of their principal action functions.
We describe some examples of classical and explicit h-transforms as particular cases of a general mechanism, which is related to the existence of symmetric diffusion operators having orthogonal polynomials as spectral decomposition.
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
Wavefunction is a fundamental concept of quantum theory. Recent studies have shown surprisingly that wavefunction can be directly reconstructed via the measurement of weak value. The weak value based direct wavefunction reconstruction not…
Transformation method provides an efficient way to control wave propagation by materials. However, the degree to which this transformation concept can be applied to other physical phenomena remains an open question. Recently, Hu et al.…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…