Related papers: Hierarchical Wave Functions Revisited
The behavior of a non-spherical particle in a viscous, plane channel flow is studied by means of a combination of analytical technique and geometrical reasoning. An efficient implementation of Lamb's general solution is adopted, allowing…
We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wave numbers satisfying…
Harmonic wave functions for integer and half-integer angular momentum are given in terms of the Euler angles $(\theta,\phi,\psi)$ that define a rotation in $SO(3)$, and the Euclidean norm in ${\mathbb R}^3$. Following a classical work by…
We study coupled acoustic and plasma waves in piezoelectric semiconductor crystals of hexagonal symmetry. We focus on the so called shear-horizontal or antiplane motions with one mechanical displacement. A set of two dimensional equations…
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrodinger equation in spaces of dimensionality higher than physical space.…
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through…
Topological wave structures -- phase vortices, skyrmions, merons, etc. -- are attracting enormous attention in a variety of quantum and classical wave fields. Surprisingly, these structures have never been properly explored in the most…
Two properties of Calogero wave functions for rational Calogero models are studied: (i) the representation of the wave functions in terms of the exponential of Lassalle operators, (ii) the $sL(2,\rr)$ structure of the Calogero--Moser wave…
We study meromorphic functions in a strip almost periodic with respect to the spherical metric. Then we get a complete description of zeros and poles for this class of functions, find a condition for a meromorphic almost periodic function…
The deuteron wave function can be presented as the table through the respective massifs of numerically values of radial wave functions. In calculations such arrays of numbers in the texts of programs to operate quite difficult. Therefore a…
Eigenvalues and wave functions describing free electron gases in toroidal shells are determined using a basis set expansion natural to the system geometry. Couplings between azimuthal and poloidal modes are found to be appreciable at lower…
We calculate the electronic wave-function for a phosphorus donor in silicon by numerical diagonalisation of the donor Hamiltonian in the basis of the pure crystal Bloch functions. The Hamiltonian is calculated at discrete points localised…
For an arbitrary solution to the AKNS hierarchy, the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method [14,21]. In this paper, we introduce a pair of wave functions of the solution…
The extended flow equations of the multi-component Toda hierarchy are constructed. We give the Hirota bilinear equations and tau function of this new extended multi-component Toda hierarchy(EMTH). Because of logarithmic terms, some extended…
The quasiparticle wavefunction of a many-electron system is traditionally defined as the eigenfunction of the quasiparticle eigenvalue equation involving the self-energy. In this article a new concept of a quasiparticle wavefunction is…
By the method of discrete transformation equations of 3-th wave hierarchy are constructed. We present in explicit form two Poisson structures, which allow to construct Hamiltonian operator consequent application of which leads to all…
The small amplitude-to-thread ratio helical configuration of a vortex filament in the ideal fluid behaves exactly as de Broglie wave. The complex-valued algebra of quantum mechanics finds a simple mechanical interpretation in terms of…
Classical geometric and topological operations on polyhedra, maps and polytopes often give rise to structures with the same symmetry group as the original one, but with more flags. In this paper we introduce the notion of voltage operations…
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…
The goal of this paper is to give an explicit computation of the curvature of the magnetic vector bundle of the multi-layer model of the fractional quantum Hall effect on a torus. We also obtain concrete formulae for the norms of the…