Related papers: Raising and lowering operators for angular momentu…
In this paper, we will assume that the structure picture of the rotation angles will be changed according to the scale of measurement (minimum measurable angle) and if we have a device with very high accuracy (high resolution) then we can…
The derivation of spherical harmonics is the same in nearly every quantum mechanics textbook and classroom. It is found to be difficult to follow, hard to understand, and challenging to reproduce by most students. In this work, we show how…
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…
Eigenfunctions of total angular momentum for a charged vector field interacting with a magnetic monopole are constructed and their properties studied. In general, these eigenfunctions can be obtained by applying vector operators to the…
In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary…
The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of…
The angular momentum formalism provides a powerful way to classify atomic states. Yet, requiring a spherical symmetry from the very first line, this formalism cannot be used for periodic systems, even though cubic semiconductor states are…
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…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
This paper claims that local space-time curvature can non-trivially contribute to the properties of orbital angular momentum in quantum mechanics. Of key importance is the demonstration that an extended orbital angular momentum operator due…
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…
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…
Relations between two definitions of (total) angular momentum operator, as a generator of rotations and in the Lagrangian formalism, are explored in quantum field theory. Generally, these definitions result in different angular momentum…
Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized…
We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and…
In this paper, we propose a new perspective of quantum spin (angular momentum) in which the Boltzmann constant \(k_{\beta}\), Planck temperature \(T_{P}\), Planck mass \(m_{P}\) and Planck area \(l_{P}^{2}\) are the integral part of the…
An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and has the familiar spectrum. The operator…
In this paper, we propose a new quantitative method for determining the state number l of the beam carry Orbital Angular Momentum (OAM), both individually and in a sum in a combination of l= -3, -2, -1, 0, 1, 2, 3 based on analysis of the…
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
Operators for simulating the scattering of two particles with spin are constructed. Three methods are shown to give the consistent lattice operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar meson, vector meson…