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 $W(x)=g\epsilon(x) x^{2n}$ and study in details the cases $n=0$ and 1. The $n=0$ superpotential is shown to lead to the known problem of two supersymmetrically related Dirac delta potentials (well and barrier). The $n=1$ case result in the potentials $V_{\pm}(x)=g^{2}x^{4}\pm2g|x|$. For $V_{-}$ we present the exact ground state solution and study the excited states by a variational technic. Starting from the ground state of $V_{-}$ and using logarithmic perturbation theory we study the ground states of $V_{+}$ and also of $V(x)=g^2 x^4$ 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