1,687 research outputs found
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
Coulomb plus power-law potentials in quantum mechanics
We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the
Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q >
-2 and q \ne 0. We show by envelope theory that the discrete eigenvalues
E_{n\ell} of H may be approximated by the semiclassical expression
E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}.
Values of mu and nu are prescribed which yield upper and lower bounds.
Accurate upper bounds are also obtained by use of a trial function of the form,
psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for
V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with
comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure
Possible Discovery Channel for New Charged Leptons at the LHC
We propose a channel for the possible discovery of new charged leptons at the
Large Hadron Collider. The proposed final state contains three same-sign
leptons, making this new channel practically back- groundless. The method is
illustrated for two different cases: the four-family Standard Model and the
Grand Unified Theory based on the E6 gauge group. An example study taking 250
GeV as the charged lepton mass shows that in both models, about 8 signal events
can be expected at 14 TeV center-of-mass energy with 1 fb^-1 of integrated
luminosity. Although the event yield might not be sufficient for detailed
measurements of the charged lepton properties, it would be sufficient to claim
discovery through a counting experiment.Comment: 8 pages, 4 figures. v2 update includes an estimate of the
backgrounds, consideration of the EW oblique parameters, and minor
improvements. v3 update includes detector acceptance and ttbar backgroun
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
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
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
Expression of the Arabidopsis WRINKLED 1 transcription factor leads to higher accumulation of palmitate in soybean seed
Soybean (Glycine max [L.] Merr.) is a commodity crop highly valued for its protein and oil content. The high percentage of polyunsaturated fatty acids in soybean oil results in low oxidative stability, which is a key parameter for usage in baking, high temperature frying applications, and affects shelf life of packaged products containing soybean oil. Introduction of a seed-specific expression cassette carrying the Arabidopsis transcription factor WRINKLED1 (AtWRI1) into soybean, led to seed oil with levels of palmitate up to approximately 20%. Stacking of the AtWRI1 transgenic allele with a transgenic locus harbouring the mangosteen steroyl-ACP thioesterase (GmFatA) resulted in oil with total saturates up to 30%. The creation of a triple stack in soybean, wherein the AtWRI1 and GmFatA alleles were combined with a FAD2-1 silencing allele led to the synthesis of an oil with 28% saturates and approximately 60% oleate. Constructs were then assembled that carry a dual FAD2-1 silencing element/GmFatA expression cassette, alone or combined with an AtWRI1 cassette. These plasmids are designated pPTN1289 and pPTN1301, respectively. Transgenic events carrying the T-DNA of pPTN1289 displayed an oil with stearate levels between 18% and 25%, and oleate in the upper 60%, with reduced palmitate
A Large Hadron Electron Collider at CERN
This document provides a brief overview of the recently published report on
the design of the Large Hadron Electron Collider (LHeC), which comprises its
physics programme, accelerator physics, technology and main detector concepts.
The LHeC exploits and develops challenging, though principally existing,
accelerator and detector technologies. This summary is complemented by brief
illustrations of some of the highlights of the physics programme, which relies
on a vastly extended kinematic range, luminosity and unprecedented precision in
deep inelastic scattering. Illustrations are provided regarding high precision
QCD, new physics (Higgs, SUSY) and electron-ion physics. The LHeC is designed
to run synchronously with the LHC in the twenties and to achieve an integrated
luminosity of O(100) fb. It will become the cleanest high resolution
microscope of mankind and will substantially extend as well as complement the
investigation of the physics of the TeV energy scale, which has been enabled by
the LHC
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