1,823 research outputs found
Criterion for polynomial solutions to a class of linear differential equation of second order
We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where
\lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential
equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n
s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}=
\lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad
s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if
\lambda_n\lambda_{n-1}\ne 0 and \delta_n=0, then the differential equation has
a polynomial solution of degree at most n. We show that the classical
differential equations of Laguerre, Hermite, Legendre, Jacobi, Chebyshev (first
and second kind), Gegenbauer, and the Hypergeometric type, etc, obey this
criterion. Further, we find the polynomial solutions for the generalized
Hermite, Laguerre, Legendre and Chebyshev differential equations.Comment: 12 page
Application of the Asymptotic Iteration Method to a Perturbed Coulomb Model
We show that the asymptotic iteration method converges and yields accurate
energies for a perturbed Coulomb model. We also discuss alternative
perturbation approaches to that model.Comment: 9 pages, 2 figures, 1 tabl
Exact solutions for vibrational levels of the Morse potential via the asymptotic iteration method
Exact solutions for vibrational levels of diatomic molecules via the Morse
potential are obtained by means of the asymptotic iteration method. It is shown
that, the numerical results for the energy eigenvalues of are all
in excellent agreement with the ones obtained before. Without any loss of
generality, other states and molecules could be treated in a similar way
Mucoid Cyst of The Penile Skin: A Rare Entity
A 9-year old male patient was admitted to our clinic for circumcision. Physical examination revealed a mass in the prepuce. After excision of the mass, histopathological examination was consistent with a mucoid cyst of the penile skin, which has been rarely reported. Pathologists and clinicians dealing with genitourinary system pathology should be familiar with this rarely encountered entity.Key Words: Mucoid cyst, penile ski
The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c
The asymptotic iteration method is applied, to calculate the angular
spheroidal eigenvalues with arbitrary complex size
parameter . It is shown that, the obtained numerical results of
are all in excellent agreement with the available
published data over the full range of parameter values , , and .
Some representative values of for large real are
also given.Comment: 15 pages, 1 figur
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
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
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
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