Quasi-Exactly Solvable Lie Superalgebras of Differential Operators (2007)
Federico Finkel, Miguel A. Rodr'iguez
In this paper, we study Lie superalgebras of 2 \Theta 2 matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension....
LIE ALGEBRAS OF DIFFERENTIAL OPERATORS AND PARTIAL INTEGRABILITY (2007)
Federico Finkel, Niky Kamran, Peter J. Olver, Miguel A. Rodr'iguez
This paper surveys recent work on Lie algebras of differential operators and their application to the construction of quasi-exactly solvable Schrodinger operators. 1
A New Algebraization of the Lamé Equation ∗ (2007)
We develop a new way of writing the Lamé Hamiltonian in Liealgebraic form. This yields, in a natural way, an explicit formula for both the Lamé polynomials and the classical non-meromorphic Lamé...
Lie Algebras Of Differential Operators And Partial Integrability (2007)
Federico Finkel, Artemio González-López, Niky Kamran, Peter J. Olver, Miguel A. Rodríguez, Miguel A. Rodr'iguez
This paper surveys recent work on Lie algebras of differential operators and their application to the construction of quasi-exactly solvable Schrodinger operators. 1 Introduction Lie-algebraic and...
Global properties of the spectrum of the Haldane-Shastry spin chain (2005)
Finkel, Federico, Gonzalez-Lopez, Artemio
We derive an exact expression for the partition function of the su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive...
On the families of orthogonal polynomials associated to the Razavy potential (1999)
Finkel, Federico, Gonzalez-Lopez, Artemio, Rodriguez, Miguel A.
We show that there are two different families of (weakly) orthogonal polynomials associated to the quasi-exactly solvable Razavy potential $V(x)=(\z \cosh 2x-M)^2$ ($\z>0$, $M\in\mathbf N$). One of...
On form-preserving transformations for the time-dependent Schr\"odinger equation (1998)
Finkel, Federico, Gonzalez-Lopez, Artemio, Kamran, Niky, Rodriguez, Miguel A.
In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schr\"odinger equation (TDSE). In...
Quasi-Exactly Solvable Time-Dependent Potentials (1997)
Finkel, Federico, Kamran, Niky
We find exact solutions of the time-dependent Schr\"odinger equation for a family of quasi-exactly solvable time-dependent potentials by means of non-unitary gauge transformations.
Quasi-exactly Solvable Lie Superalgebras of Differential Operators (1997)
Finkel, Federico, González-López, Artemio, Rodríguez, Miguel A.
In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension....
Finkel, Federico, Kamran, Niky
We prove that the scalar and $2\times 2$ matrix differential operators which preserve the simplest scalar and vector-valued polynomial modules in two variables have a fundamental Lie algebraic...
Lie Algebras of Differential Operators and Partial Integrability (1996)
Finkel, Federico, Gonzalez-Lopez, Artemio, Kamran, Niky, Olver, Peter J., Rodriguez, Miguel A.
This paper surveys recent work on Lie algebras of differential operators and their application to the construction of quasi-exactly solvable Schroedinger operators.
Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials (1996)
Finkel, Federico, Gonzalez-Lopez, Artemio, Rodriguez, Miguel A.
In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey...
Quasi-Exactly Solvable Spin 1/2 Schr\"odinger Operators (1995)
Finkel, Federico, Gonzalez-Lopez, Artemio, Rodriguez, Miguel A.
The algebraic structures underlying quasi-exact solvability for spin 1/2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order...
Quasi-exactly solvable spin 1=2 Schrodinger operators, preprint, Universidad Complutense (1995)
Federico Finkel, Miguel A. Rodr'iguez
The algebraic structures underlying quasi-exact solvability for spin 1=2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order...