Related papers: Calculating spherical harmonics without derivative…
Electrodynamic spherical harmonic is a second rank tensor in three-dimensional space. It allows to separate the radial and angle variables in vector solutions of Maxwell's equations. Using the orthonormalization for electrodynamic spherical…
The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
In this work, we use semigroup integral to evaluate zeta-function regularized determinants. This is especially powerful for non--positive operators such as the Dirac operator. In order to understand fully the quantum effective action one…
We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…
Symmetry underlies many of the most effective classical and quantum learning algorithms, yet whether quantum learners can gain a fundamental advantage under symmetry-imposed structures remains an open question. Based on evidence that…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…
In terms of the telescoping method, a simple binomial sum is given. By applying the derivative operators to the equation just mentioned, we establish several general harmonic number identities including some known results.
The orbital angular momentum operator expansion turns to be a powerful tool to construct the fully covariant partial wave amplitudes of hadron decay reactions and hadron photo- and electroproduction processes. In this paper we consider a…
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
Three sets of ladder operators in spheroconal coordinates and their respective actions on Lam\'e spheroconal harmonic polynomials are presented in this article. The polynomials are common eigenfunctions of the square of the angular momentum…
We consider the symmetry algebra generated by the total angular momentum operators, appearing as constants of motion of the $\mathrm{S}_3$ Dunkl Dirac equation. The latter is a deformation of the Dirac equation by means of Dunkl operators,…
A systematic method for calculating higher-order corrections of the relativistic semiclassical fixed-energy amplitude is given. The central scheme in computing corrections of all orders is related to a time ordering operation of an operator…
We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular momentum eigenstates. We split, from the total angular momentum operator, a proper part which can be separately…
Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum…
I show how applying a symplectic Gram-Schmidt orthogonalization to the normalizer of a quantum code gives a different way of determining the code's logical operators. This approach may be more natural in the setting where we produce a…