36 research outputs found
Approximate solution for Fokker-Planck equation
In this paper, an approximate solution to a specific class of the
Fokker-Planck equation is proposed. The solution is based on the relationship
between the Schr\"{o}dinger type equation with a partially confining and
symmetrical potential. To estimate the accuracy of the solution, a function
error obtained from the original Fokker-Planck equation is suggested. Two
examples, a truncated harmonic potential and non-harmonic polynomial, are
analyzed using the proposed method. For the truncated harmonic potential, the
system behavior as a function of temperature is also discussed.Comment: 12 pages, 8 figure
Supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian Screened Coulomb potential via Hamiltonian hierarchy inspired variational method
The supersymmetric solutions of PT-symmetric and Hermitian/non-Hermitian
forms of quantum systems are obtained by solving the Schrodinger equation for
the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy
inspired variational method is used to obtain the approximate energy
eigenvalues and corresponding wave functions.Comment: 13 page
Ladder operators for subtle hidden shape invariant potentials
Ladder operators can be constructed for all potentials that present the
integrability condition known as shape invariance, satisfied by most of the
exactly solvable potentials. Using the superalgebra of supersymmetric quantum
mechanics we construct the ladder operators for two exactly solvable potentials
that present a subtle hidden shape invariance.Comment: 9 pages, based on the talk given at International Conference Progress
in Supersymmetric Quantum Mechanics (PSQM03), Valladolid, Spain, 15-19 July,
2003, to appear in a Special Issue of J. Phys. A: Math. Ge
Generalized Ladder Operators for Shape-invariant Potentials
A general form for ladder operators is used to construct a method to solve
bound-state Schr\"odinger equations. The characteristics of supersymmetry and
shape invariance of the system are the start point of the approach. To show the
elegance and the utility of the method we use it to obtain energy spectra and
eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials
and for the radial harmonic oscillator and Coulomb potentials.Comment: in Revte
Breather Stability in One Dimensional Lattices with a Symmetric Morse Potential
Harmonic one dimensional lattice with an additional Morse potential on site has been used to describe DNA macromolecules properties. We analyze a modification of this lattice introducing a symmetric Morse potential. The existence and stability of the breather is studied in this modified system. We obtain harmonic bifurcation and determine the effective mass of the mobile breather
An Algebraic q-Deformed Form for Shape-Invariant Systems
A quantum deformed theory applicable to all shape-invariant bound-state
systems is introduced by defining q-deformed ladder operators. We show these
new ladder operators satisfy new q-deformed commutation relations. In this
context we construct an alternative q-deformed model that preserve the
shape-invariance property presented by primary system. q-deformed
generalizations of Morse, Scarf, and Coulomb potentials are given as examples
A new simple class of superpotentials in SUSY Quantum Mechanics
In this work we introduce the class of quantum mechanics superpotentials
and study in details the cases and 1. The
superpotential is shown to lead to the known problem of two
supersymmetrically related Dirac delta potentials (well and barrier). The
case result in the potentials . For we
present the exact ground state solution and study the excited states by a
variational technic. Starting from the ground state of and using
logarithmic perturbation theory we study the ground states of and also
of and compare the result got by this new way with other results
for this state in the literature.Comment: 18 page
Selenium biochemistry and its role for human health
Despite its very low level in humans, selenium plays an important and unique role among the (semi)metal trace essential elements because it is the only one for which incorporation into proteins is genetically encoded, as the constitutive part of the 21st amino acid, selenocysteine. Twenty-five selenoproteins have been identified so far in the human proteome. The biological functions of some of them are still unknown, whereas for others there is evidence for a role in antioxidant defence, redox state regulation and a wide variety of specific metabolic pathways. In relation to these functions, the selenoproteins emerged in recent years as possible biomarkers of several diseases such as diabetes and several forms of cancer. Comprehension of the selenium biochemical pathways under normal physiological conditions is therefore an important requisite to elucidate its preventing/therapeutic effect for human diseases. This review summarizes the most recent findings on the biochemistry of active selenium species in humans, and addresses the latest evidence on the link between selenium intake, selenoproteins functionality and beneficial health effects. Primary emphasis is given to the interpretation of biochemical mechanisms rather than epidemiological/observational data. In this context, the review includes the following sections: (1) brief introduction; (2) general nutritional aspects of selenium; (3) global view of selenium metabolic routes; (4) detailed characterization of all human selenoproteins; (5) detailed discussion of the relation between selenoproteins and a variety of human diseases