1,709 research outputs found
Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method
For non-zero 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 and 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
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