Analytical solution to the Schrodinger equation of a laser-driven correlated two-particle system

The time-dependent quantum system of two laser-driven electrons in a harmonic oscillator potential is analysed, taking into account the repulsive Coulomb interaction between both particles. The Schrodinger equation of the two-particle system is shown to be analytically soluble in case of arbitrary laser frequencies and individual oscillator frequencies, defining the system. Quantum information processing could be a possible field of applicationComment: 5 page

Analytic Solution of a Relativistic Two-dimensional Hydrogen-like Atom in a Constant Magnetic Field

We obtain exact solutions of the Klein-Gordon and Pauli Schroedinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular values of the magnetic field strength. The results are compared to those obtained in the non-relativistic and spinless case. We obtain that the relativistic spectrum does not present s states.Comment: RevTeX, 8 pages, to be published in Phys. Lett.

Cardiovascular Attributable Risk and Risk Factors Evaluations as a Matter of Statistics and Data Mining Confluences

Cardiovascular diseases represent a severe threat for humanity, being the first cause of death and hospitalization in both genders. An impressive number of studies have been developed in order to identify a set of factors causing this kind of illness, but only few of them were able to pay significant resources in analyzing large population samples (tens of thousands) and for longer periods of time (decades). This paper’s objective is to continue the previous researches of the eProCord project and to validate with concrete data the theoretical model developed for the attributable risk (AR). It will consider the same risk factors for myocardial infarction identified by INTERHEART study and the same work hypothesis. We will also evaluate if a certain value of the AR is also confirmed by the invoked disease of the patient. Using statistical and data mining tools we will investigate the prediction potential of the chosen factors and the opportunity to extend them in order to capture any cardiovascular disease. The empirical tests rely for now on a sample of 236 patients.Cardiovascular Disease, Myocardial Infarction, Attributable Risk, Roc, Data Mining, Classification

Distortion of Wigner molecules : pair function approach

We considered a two dimensional three electron quantum dot in a magnetic field in the Wigner limit. A unitary coordinate transformation decouples the Hamiltonian (with Coulomb interaction between the electrons included) into a sum of three independent pair Hamiltonians. The eigen-solutions of the pair Hamiltonian provide a spectrum of pair states. Each pair state defines the distance of the two electrons involved in this state. In the ground state for given pair angular momentum $m$, this distance increases with increasing $|m|$. The pair states have to be occupied under consideration of the Pauli exclusion principle, which differs from that for one-electron states and depends on the total spin $S$ and the total orbital angular momentum $M_L=\sum m_i$ (sum over all pair angular momenta). We have shown that the three electrons in the ground state of the Wigner molecule form an equilateral triangle (as might be expected) only, if the state is a quartet ($S=3/2$) and the orbital angular momentum is a magic quantum number ($M_L=3 m ; m=$ integer). Otherwise the triangle in the ground state is isosceles. For $M_L=3 m+1$ one of the sides is longer and for $M_L=3 m-1$ one of the sides is shorter than the other two

Charged particles in external fields as physical examples of quasi-exactly solvable models: a unified treatment

We present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged particles in an external oscillator potential. We show that all these cases are reducible to the same basic equation, which is quasi-exactly solvable owing to the existence of a hidden $sl_2$ algebraic structure. A systematic and unified algebraic solution to the basic equation using the method of factorization is given. Analytic expressions of the energies and the allowed frequencies for the three cases are given in terms of the roots of one and the same set of Bethe ansatz equations.Comment: RevTex, 15 pages, no figure

The use of external evaluative information with formative means: the case of chilean educative establisments participants of the SEPA

En el presente trabajo se desarrolla una investigación que indaga sobre las diversas formas en que se puede utilizar información evaluativa acerca del aprendizaje de los alumnos, y los factores que facilitan y dificultan su uso, en un grupo de establecimientos educacionales que participan del Sistema de Evaluación de Progresos del Aprendizaje (SEPA), desarrollado e implementado por el Centro de Medición MIDE UC de la Pontificia Universidad Católica de Chile. Basada en nuestra experiencia previa y la literatura anticipamos dificultades de comprensión y de uso de la información SEPA por parte de los establecimientos participantes. Se conduce una investigación exploratorio-descriptiva mediante entrevistas semi-estructuradas a 14 directivos y profesores pertenecientes a siete establecimientos educacionales adheridos a SEPA. Tal como esperabamos, se observa una comprensión parcial de los indicadores introducidos, particularmente de aquellos más complejos (valor agregado). Se constata que la relación que los actores establecen con la información evaluativa depende de las características de la organización y de sus protagonistas. Se detectan diversos tipos de uso de la información, los cuales se clasifican como instrumental, legitimante, persuasivo, simbolico y conceptual. Nuestros hallazgos comprueban investigaciones previas que la introducción de información evaluativa es solamente el primer paso en el proceso complejo necesario para influir el mejoramiento escola

Violation of non-interacting V\cal V-representability of the exact solutions of the Schr\"odinger equation for a two-electron quantum dot in a homogeneous magnetic field

We have shown by using the exact solutions for the two-electron system in a parabolic confinement and a homogeneous magnetic field [ M.Taut, J Phys.A{\bf 27}, 1045 (1994) ] that both exact densities (charge- and the paramagnetic current density) can be non-interacting $\cal V$-representable (NIVR) only in a few special cases, or equivalently, that an exact Kohn-Sham (KS) system does not always exist. All those states at non-zero $B$ can be NIVR, which are continuously connected to the singlet or triplet ground states at B=0. In more detail, for singlets (total orbital angular momentum $M_L$ is even) both densities can be NIVR if the vorticity of the exact solution vanishes. For $M_L=0$ this is trivially guaranteed because the paramagnetic current density vanishes. The vorticity based on the exact solutions for the higher $|M_L|$ does not vanish, in particular for small r. In the limit $r \to 0$ this can even be shown analytically. For triplets ($M_L$ is odd) and if we assume circular symmetry for the KS system (the same symmetry as the real system) then only the exact states with $|M_L|= 1$ can be NIVR with KS states having angular momenta $m_1=0$ and $|m_2|=1$. Without specification of the symmetry of the KS system the condition for NIVR is that the small-r-exponents of the KS states are 0 and 1.Comment: 18 pages, 4 figure