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It is shown that the higher order supersymmetric partners of the harmonic oscillator Hamiltonian provide the simplest non-trivial realizations of the polynomial Heisenberg algebras. A linearized version of the corresponding annihilation and creation operator leads to a Fock representation which is the same as for the harmonic oscillator Hamiltonian. 1.… (More)

- David J. Fernández, Dean J. Tuma, Pamela L. Tuma
- American journal of physiology. Gastrointestinal…
- 2012

Although alcoholic liver disease is clinically well described, the molecular basis for alcohol-induced hepatotoxicity is not well understood. Previously, we found that alcohol exposure led to increased microtubule acetylation and stability in polarized, hepatic WIF-B cells and in livers from ethanol-fed rats. Because microtubules are known to regulate… (More)

- Blythe D. Shepard, David J. Fernández, Pamela L. Tuma
- Genes & Nutrition
- 2009

Alcoholic liver disease is a major biomedical health concern in the United States. Despite considerable research efforts aimed at understanding the progression of the disease, the specific mechanisms leading to alcohol-induced damage remain elusive. Numerous proteins are known to have alcohol-induced alterations in their dynamics. Defining these defects in… (More)

- David J. Fernández, Bogdan Mielnik, Oscar Rosas–Ortiz, Boris F. Samsonov
- 2003

For a class of Schrödinger Hamiltonians the supersymmetry transformations can degenerate to simple coordinate displacements. We examine this phenomenon and show that it distinguishes the Weierstrass potentials including the one-soliton wells and periodic Lamé functions. A supersymmetric sense of the addition formula for the Weierstrass functions is… (More)

- David J. Fernández, E. Salinas-Hernández, Adolfo López Mateos
- 2005

The confluent second-order supersymmetric quantum mechanics, with factorization energies ǫ1, ǫ2 tending to a single ǫ-value, is studied. We show that the Wronskian formula remains valid if generalized eigenfunctions are taken as seed solutions. The confluent algorithm is used to generate SUSY partners of the Coulomb potential.

We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order SUSY transformations are used to derive in a simple way the higher-order case. The second order technique is addressed directly, and through this approach unexpected… (More)

A systematic procedure to derive exact solutions of the associated Lamé equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are used to generate new exactly solvable potentials; some of them exhibit an interesting property of periodicity defects.

- David J. Fernández, Benita L. McVicker, Dean J. Tuma, Pamela L. Tuma
- Biochemical pharmacology
- 2009

Although alcoholic liver disease is clinically well-described, the molecular basis for alcohol-induced hepatotoxicity is not well understood. Previously, we determined that the clathrin-mediated internalization of asialoglycoprotein receptor was impaired in ethanol-treated WIF-B cells whereas the internalization of a glycophosphatidylinositol-anchored… (More)

Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first and second order for one-dimensional arbitrary systems, and we will illustrate the method through the trigonometric… (More)

- Alonso Contreras-Astorga, David J. Fernández
- 2008

The first and second-order supersymmetry transformations are used to generate Hamiltonians with known spectra departing from the trigonometric Pöschl-Teller potentials. The several possibilities of manipulating the initial spectrum are fully explored, and it is shown how to modify one or two levels, or even to leave the spectrum unaffected. The behavior of… (More)