Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method

For non-zero $\ell$ values, we present an analytical solution of the radial Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris approximation within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and corresponding wave functions are obtained for a number of diatomic molecules and the results are compared with the findings of the super-symmetry, the hypervirial perturbation, the Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of Physics A: Mathematical and Genera

Masses and decay constants of bound states containing fourth family quarks from QCD sum rules

The heavy fourth generation of quarks that have sufficiently small mixing with the three known SM families form hadrons. In the present work, we calculate the masses and decay constants of mesons containing either both quarks from the fourth generation or one from fourth family and the other from known third family SM quarks in the framework of the QCD sum rules. In the calculations, we take into account two gluon condensate diagrams as nonperturbative contributions. The obtained results reduce to the known masses and decay constants of the $\bar b b$ and $\bar c c$ quarkonia when the fourth family quark is replaced by the bottom or charm quark.Comment: 15 Pages, 9 Figures and 6 Table

Solvable Systems of Linear Differential Equations

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.Comment: 13 page

Review of Linac-Ring Type Collider Proposals

There are three possibly types of particle colliders schemes: familiar (well known) ring-ring colliders, less familiar however sufficiently advanced linear colliders and less familiar and less advanced linac-ring type colliders. The aim of this paper is two-fold: to present possibly complete list of papers on linac-ring type collider proposals and to emphasize the role of linac-ring type machines for future HEP research.Comment: quality of figures is improved, some misprints are correcte

Two-dimensional random walk in a bounded domain

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex

Fourth Generation Pseudoscalar Quarkonium Production and Observability at Hadron Colliders

The pseudoscalar quarkonium state, eta_4 1^S_0, formed by the Standard Model (SM) fourth generation quarks, is the best candidate among the fourth generation quarkonia to be produced at the LHC and VLHC. The production of this J^{PC} = 0^{-+} resonance is discussed and the background processes are studied to obtain the integrated luminosity limits for the discovery, depending on its mass.Comment: 13 pages, 4 figures, 5 table

An Improvement of the Asymptotic Iteration Method for Exactly Solvable Eigenvalue Problems

We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the Nikiforov--Uvarov methods, which both solve the second order linear ordinary differential equations analytically.Comment: RevTex4, 8 page

d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.Comment: 14 pages, no figures, to appear in J. Phys. A: Math. Ge

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Quarkonium and hydrogen spectra with spin dependent relativistic wave equation

A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently the Dirac matrices and the k operator of Dirac's theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin 1/2 bound state single electron in Coulomb potential and then further extended to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.Comment: 14 pages, v7: Journal reference adde