Related papers: Generalized Spherical Harmonics
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
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…
The angular momentum quantum number L of spherical harmonic Y_l_,_m based on an associated Legendre polynomial is nonnegative integer 0 1 2 ... and must never be a fraction. But the study in this paper found that the quantum number L…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…
In this paper, we present the implicit equations for one special class of real-valued spherical harmonics with octahedral symmetry. Based on this representation, we construct the rotationally invariant measure of deviation from the…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation,…
We present a generalized information-theoretic measure of synchronization in quantum systems. This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks. Furthermore, the new measure…
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
The article contains several observations on spherical harmonics and their nodal sets: a construction for harmonics with prescribed zeroes; a kind of canonical representation of this type for harmonics on $\bbS^2$; upper and lower bounds…
In this paper we provide some simple characterizations for the spherical harmonics coefficients of an isotropic random field on the sphere. The main result is a characterization of isotropic gaussian fields through independence of the…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…
The associated Legendre functions $P_{l}^{(m)}(x)$ for a given $l-m$, may be taken into account as the increasing infinite sequences with respect to both indices $l$ and $m$. This allows us to construct the exponential generating functions…
The azimuthal and magnetic quantum numbers of spherical harmonics $Y_{l}^{m}(\theta,\phi)$ describe quantization corresponding to the magnitude and $z$-component of angular momentum operator in the framework of realization of $su(2)$ Lie…
In this paper the general solution of the quantum damped harmonic oscillator is given.
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the…