Related papers: Harmonic Oscillators and Elementary Particles
We evaluate the matrix elements $<r^{p}>$ for the $n$ -dimensional harmonic oscillator in terms of the dual Hahn polynomials and derive a corresponding three-term recurrence relation and a Pasternack-type reflection relation. A short review…
The SU(3)_flavor constituent quark model has been quite successful to explain the properties as well as the observed spectrum of mesons with pseudoscalar and vector quantum numbers. Many radial and orbital excitations of quark-antiquark…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
All known elementary vector particles, the photon, Z, W and the gluons, are described by the gauge theory. They belong to the real representation (1/2,1/2) of the Lorentz group. On the other hand inequivalent representations (1,0) and (0,1)…
Exotic elementary objects such as "holons" and "spinons", which are widely used in descriptions of correlated electrons in reduced spatial dimensions, were introduced from analysis of the excitation branches of one-dimensional (1D) models.…
In a recent publication, we proposed two possible wave functions for the elementary excitations of the SU(3) Haldane--Shastry model (HSM), but argued on very general grounds that only one or the other can be a valid excitation. Here we…
We proposed a unified framework to describe the interactions of the observed $T_{cc}$, $P_c$, and $P_{cs}$ within a quark level interaction in our previous work. In this work, we generalize our framework to the loosely bound hadronic…
We consider a well-known static, axially symmetric, vacuum solution of Einstein equations belonging to Weyl's class and determine the fundamental frequencies of small harmonic oscillations of test particles around stable circular orbits in…
We show a symmetry that, in the context of a composite Higgs with anarchic flavor, can suppress the dominant CP violating contributions to $K-\bar K$ mixing. Based on previous extensions of SU(3)$_c$, we consider the case in which the…
The set of trajectories for massive spinless particles on $AdS_{N+1}$ spacetime is described by the dynamical integrals related to the isometry group SO(2,N). The space of dynamical integrals is mapped one to one to the phase space of the…
The harmonic quarks and their complete oscillators are presenting the unprecedented exact solution for the mass spectrum of mesons with an explicit charm. The experimental and calculated spectrums coincide with standard deviation in 1.8…
In the Elliott SU(3) symmetry scheme the single particle basis is derived from the isotropic harmonic oscillator Hamiltonian in the Cartesian coordinate system. These states are transformed into the solutions of the same Hamiltonian within…
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative…
A composite model of quarks and bosons is proposed in which a spin $1/2$ isospin doublet $\psi$ is the basic building block of quarks and bosons in the standard model. The $\psi$ has two components $v$ and $w$ with charges $Q=\frac{1}{3}e$…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location…
In the first part of this talk it is discussed why observed neutrino oscillations (which suggest the existence of right-handed neutrinos with certain Dirac and Majorana masses) seem to select out the route to higher unification based on the…
In one-dimensional bosonic quantum mixtures with SU(2)-symmetry breaking Hamiltonian, the dynamical evolution explores different particle exchange symmetry sectors. For the case of infinitely strong intra-species repulsion, the hallmark of…
For the symmetric harmonic oscillator and the symmetric bouncer defined in 2-D, two different Hamiltonian are given describing the same classical dynamics; however, their quantum dynamics behavior are different.