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

Renormalized Bosonic Interaction of Excitons

An effective bosonic Hamiltonian of $1s$ excitons with ``spin'' degrees of freedom in two dimension is obtained through a projection procedure, starting from a conventional electron-hole Hamiltonian ${\cal H}_{eh}$. We first demonstrate that a straightforward transformation of ${\cal H}_{eh}$ into a Hamiltonian of bosonic excitons does not give the two-body interaction between an ``up-spin'' exciton and a ``down-spin'' exciton, which are created by the left- and right-circularly polarized light beams, respectively. We then show that this interaction is generated through a projection procedure onto the subspace spanned by $1s$ excitons, as a renormalization effect coming from higher exciton states. The projection also renormalizes the interaction between $1s$ excitons with the same spins by a large amount. These renormalization effects are crucial for the polarization dependence of the optical responses from semiconductors. The present theory gives the microscopic foundation of the phenomenology that was successfully applied to the analysis of four-wave mixing experiments in GaAs quantum wells strongly coupled to the radiation field in a high-Q micro cavity.Comment: 2 figure

Anales del III Congreso Internacional de Vivienda y Ciudad "Debate en torno a la nueva agenda urbana"

Acta de congresoEl III Congreso Internacional de Vivienda y Ciudad “Debates en torno a la NUEVa Agenda Urbana”, ha sido una apuesta de alto compromiso por acercar los debates centrales y urgentes que tensionan el pleno ejercicio del derecho a la ciudad. Para ello las instituciones organizadoras (INVIHAB –Instituto de Investigación de Vivienda y Hábitat y MGyDH-Maestría en Gestión y Desarrollo Habitacional-1), hemos convidado un espacio que se concretó con potencia en un debate transdisciplinario. Convocó a intelectuales de prestigio internacional, investigadores, académicos y gestores estatales, y en una metodología de innovación articuló las voces académicas con las de las organizaciones sociales y/o barriales en el Foro de las Organizaciones Sociales que tuvo su espacio propio para dar voz a quienes están trabajando en los desafíos para garantizar los derechos a la vivienda y los bienes urbanos en nuestras ciudades del Siglo XXI

Finite fractal dimensional global attractor for abstract differential equations with state-dependent delay.

We study the existence of a finite fractal dimensional global attractor for the multivalued semigroup generated by a general class of abstract differential equations with state-dependent delay. In the last section, some examples concerning partial differential equations with state-dependent delay are presented

An unusual intramolecular trans-amidation

Polyketide biosynthesis engages a series of well-timed biosynthetic operations to generate elaborate natural products from simple building blocks. Mimicry of these processes has offered practical means for total synthesis and provided a foundation for reaction discovery. We now report an unusual intramolecular trans-amidation reaction discovered while preparing stabilized probes for the study of actinorhodin biosynthesis. This rapid cyclization event offers insight into the natural cyclization process inherent to the biosynthesis of type II polyketide antibiotics