4,737 research outputs found
On algebraic classification of quasi-exactly solvable matrix models
We suggest a generalization of the Lie algebraic approach for constructing
quasi-exactly solvable one-dimensional Schroedinger equations which is due to
Shifman and Turbiner in order to include into consideration matrix models. This
generalization is based on representations of Lie algebras by first-order
matrix differential operators. We have classified inequivalent representations
of the Lie algebras of the dimension up to three by first-order matrix
differential operators in one variable. Next we describe invariant
finite-dimensional subspaces of the representation spaces of the one-,
two-dimensional Lie algebras and of the algebra sl(2,R). These results enable
constructing multi-parameter families of first- and second-order quasi-exactly
solvable models. In particular, we have obtained two classes of quasi-exactly
solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge
A New Algebraization of the Lame Equation
We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form.
This yields, in a natural way, an explicit formula for both the Lame
polynomials and the classical non-meromorphic Lame functions in terms of
Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page
A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry
We develop a systematic algorithm for constructing an N-fold supersymmetric
system from a given vector space invariant under one of the supercharges.
Applying this algorithm to spaces of monomials, we construct a new
multi-parameter family of N-fold supersymmetric models, which shall be referred
to as "type C". We investigate various aspects of these type C models in
detail. It turns out that in certain cases these systems exhibit a novel
phenomenon, namely, partial breaking of N-fold supersymmetry.Comment: RevTeX 4, 28 pages, no figure
Quasi-exactly Solvable Lie Superalgebras of Differential Operators
In this paper, we study Lie superalgebras of matrix-valued
first-order differential operators on the complex line. We first completely
classify all such superalgebras of finite dimension. Among the
finite-dimensional superalgebras whose odd subspace is nontrivial, we find
those admitting a finite-dimensional invariant module of smooth vector-valued
functions, and classify all the resulting finite-dimensional modules. The
latter Lie superalgebras and their modules are the building blocks in the
construction of QES quantum mechanical models for spin 1/2 particles in one
dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page
On the families of orthogonal polynomials associated to the Razavy potential
We show that there are two different families of (weakly) orthogonal
polynomials associated to the quasi-exactly solvable Razavy potential V(x)=(\z
\cosh 2x-M)^2 (\z>0, ). One of these families encompasses the
four sets of orthogonal polynomials recently found by Khare and Mandal, while
the other one is new. These results are extended to the related periodic
potential U(x)=-(\z \cos 2x -M)^2, for which we also construct two different
families of weakly orthogonal polynomials. We prove that either of these two
families yields the ground state (when is odd) and the lowest lying gaps in
the energy spectrum of the latter periodic potential up to and including the
gap and having the same parity as . Moreover, we show
that the algebraic eigenfunctions obtained in this way are the well-known
finite solutions of the Whittaker--Hill (or Hill's three-term) periodic
differential equation. Thus, the foregoing results provide a Lie-algebraic
justification of the fact that the Whittaker--Hill equation (unlike, for
instance, Mathieu's equation) admits finite solutions.Comment: Typeset in LaTeX2e using amsmath, amssymb, epic, epsfig, float (24
pages, 1 figure
Action-Research, Professional Development of the Physical Education Teachers in Rural Schools
La finalidad de este estudio es analizar la influencia de un grupo de trabajo de Investigación-Acción en el desarrollo profesional de maestros de Educación Física (EF) que ejercen su labor docente en la Escuela Rural.
El diseño es un estudio multicaso. Para la recogida de datos se utilizaron: historias de vida, entrevistas en profundidad, análisis de documentos y diario de investigación. El análisis de datos se realizó a través de un proceso de categorización.
Los resultados muestran que: (a)-los maestros de EF que ejercen su labor docente en la escuela rural pasan por situaciones difíciles y complicadas los primeros años, y que la pertenencia a grupos de Investigación-Acción les
ayuda a que la adaptación a este contexto educativo sea más rápida y fácil; (b)-la metodología de Investigación-Acción genera procesos de reflexión que ayudan a mejorar su práctica docente, influye positivamente en su desarrollo profesional y supone un apoyo.The purpose of this paper is to analyze the influence of a Action Research group on professional development of physical education (PE) teachers in rural school. The research methodology used was case study. Data collection was conducted through interviews, life stories, document analysis and research notebook. Data analysis was performed through a categorization process.
The results show that: (a)-PEF teachers in rural school engaged in difficult situations at early years, and to be a membership of Action Research group helps them adapt to this context educational faster and easier, (b)-the Action Research methodology generates reflective processes that help improve their teaching, has a positive influence on their professional development and represent a suppor
New Algebraic Quantum Many-body Problems
We develop a systematic procedure for constructing quantum many-body problems
whose spectrum can be partially or totally computed by purely algebraic means.
The exactly-solvable models include rational and hyperbolic potentials related
to root systems, in some cases with an additional external field. The
quasi-exactly solvable models can be considered as deformations of the previous
ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page
Quasi-exact solvability beyond the SL(2) algebraization
We present evidence to suggest that the study of one dimensional
quasi-exactly solvable (QES) models in quantum mechanics should be extended
beyond the usual \sla(2) approach. The motivation is twofold: We first show
that certain quasi-exactly solvable potentials constructed with the \sla(2)
Lie algebraic method allow for a new larger portion of the spectrum to be
obtained algebraically. This is done via another algebraization in which the
algebraic hamiltonian cannot be expressed as a polynomial in the generators of
\sla(2). We then show an example of a new quasi-exactly solvable potential
which cannot be obtained within the Lie-algebraic approach.Comment: Submitted to the proceedings of the 2005 Dubna workshop on
superintegrabilit
Quasi-exactly solvable quartic potential
A new two-parameter family of quasi-exactly solvable quartic polynomial
potentials is introduced. Until now,
it was believed that the lowest-degree one-dimensional quasi-exactly solvable
polynomial potential is sextic. This belief is based on the assumption that the
Hamiltonian must be Hermitian. However, it has recently been discovered that
there are huge classes of non-Hermitian, -symmetric Hamiltonians
whose spectra are real, discrete, and bounded below [physics/9712001].
Replacing Hermiticity by the weaker condition of symmetry allows
for new kinds of quasi-exactly solvable theories. The spectra of this family of
quartic potentials discussed here are also real, discrete, and bounded below,
and the quasi-exact portion of the spectra consists of the lowest
eigenvalues. These eigenvalues are the roots of a th-degree polynomial.Comment: 3 Pages, RevTex, 1 Figure, encapsulated postscrip
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