The confluent second-order supersymmetric quantum mechanics, with factorization energies ǫ 1 , ǫ 2 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)
The first and second-order supersymmetry transformations are used to generate Ha-miltonians 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)
Using the modified factorization method employed in , we construct a new class of radial potentials whose spectrum for l = 0 coincides exactly with that of the hydrogen atom. A limiting case of our family coincides with the potentials previously derived by Abraham and Moses .
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)
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)
Coherent states are derived for one-dimensional systems generated by su-persymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated to the isospectral part or the spectrum.… (More)
The confluent algorithm, a degenerate case of the second order supersymmetric quantum mechanics, is studied. It is shown that the transformation function must asymptotically vanish to induce non-singular final potentials. The technique can be used to create a single level above the initial ground state energy. The method is applied to the free particle,… (More)
By using a matrix technique, which allows to identify directly the ladder operators, the Penning trap coherent states are derived as eigenstates of the appropriate annihilation operators. These states are compared with the ones obtained through the displacement operator. The associated wave functions and mean values for some relevant operators in these… (More)
Alcoholic liver disease has been clinically well described, but the molecular mechanisms leading to hepatotoxicity have not been fully elucidated. Previously, we determined that microtubules are hyperacetylated and more stable in ethanol-treated WIF-B cells, VL-17A cells, liver slices, and in livers from ethanol-fed rats. From our recent studies, we believe… (More)