Related papers: Spherical to Cartesian Coordinates Transformation …
Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.
We consider the normal operator of the X-ray transform, weighted with Gaussian weights, in Euclidean space with dimension at least 3. We show the eigenfunctions of the normal operator are joint eigenfunctions of the harmonic oscillator and…
The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory.…
We perform an unitary transformation for the symmetric phonon mode of the Holstein molecular crystal hamiltonian. We show how to compute the electronic spectral functions by exact numerical diagonalisation of an effective hamiltonian fully…
The confluent second-order supersymmetric quantum mechanics, in which the factorization energies tend to a common value, is used to generate Hamiltonians with known spectra departing from the hyperbolic Rosen-Morse and Eckart potentials.…
We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…
The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties,…
Discrete interaction models for the classical harmonic oscillator are used for introducing new mathematical generalizations in the usual continuous formalism. The inverted harmonic potential and generalized discrete hyperbolic and…
We discuss solutions of the spherically symmetric wave equation and Klein Gordon equation in an arbitrary number of spatial and temporal dimensions. Starting from a given solution, we present various procedures to generate futher solutions…
A time operator $\hat T_\eps$ of the one-dimensional harmonic oscillator $ \hat h_\eps=\half(p^2+\eps q^2)$ is rigorously constructed. It is formally expressed as $ \hat T_\eps=\half\frac{1}{\sqrt \eps } (\arctan (\sqrt \eps \hat…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…
Spherical Harmonics, $Y_\ell^m(\theta,\phi)$, are derived and presented (in a Table) for half-odd-integer values of $\ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the…
We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit…
A new single-particle shell model is derived by solving the Schr\"odinger equation for a semi-spheroidal potential well. Only the negative parity states of the $Z(z)$ component of the wave function are allowed, so that new magic numbers are…
We employ the framework of operational calculus to derive the operators associated with the spherical mean and a class of related averaging means of a function in $n$-dimensional space. Beginning with the classical definition of the…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical…