0 On the relation between polynomial deformations of sl ( 2 , R ) and quasi - exactly solvability
نویسنده
چکیده
A general method based on the polynomial deformations of the Lie algebra sl(2, R) is proposed in order to exhibit the quasi-exactly solv-ability of specific Hamiltonians implied by quantum physical models. This method using the finite-dimensional representations and differential realizations of such deformations is illustrated on the sextic oscillator as well as on the second harmonic generation.
منابع مشابه
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 sl(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the sl(2) Lie algebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is do...
متن کاملLie - algebraic approach to the theory of polynomial solutions . III . Differential equations in two real variables
Classification theorems for linear differential equations in two real variables, possessing eigenfunctions in the form of the polynomi-als (the generalized Bochner problem) are given. The main result is based on the consideration of the eigenvalue problem for a polynomial elements of the universal enveloping algebras of the algebras sl 3 (R), sl 2 (R) ⊕ sl 2 (R) and gl 2 (R) ⊲< R r+1 , r > 0 ta...
متن کاملQuasi-exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is a physical example of quasi-exactly solvable systems. This model, however, does not belong to the classes based on the algebra sl(2) which underlies most one-dimensional and effectively one-dimensional quasi-exactly solvable systems. In this paper we demonstrate that the quasi-exactly ...
متن کاملQuasi-exact Solvability of Dirac Equations
We present a general procedure for determining quasi-exact solvability of the Dirac and the Pauli equation with an underlying sl(2) symmetry. This procedure makes full use of the close connection between quasi-exactly solvable systems and supersymmetry. The Dirac-Pauli equation with spherical electric field is taken as an example to illustrate the procedure. 1. In this talk we present a general...
متن کاملar X iv : h ep - t h / 96 11 22 6 v 1 2 7 N ov 1 99 6 On the relations between osp ( 2 , 2 ) and the quasi exactly solvable systems
By taking a product of two sl(2) representations, we obtain the differential operators preserving some space of polynomials in two variables. This allows us to construct the representations of osp(2,2) in terms of matrix differential operators in two variables. The corresponding operators provide the building blocks for the construction of quasi exactly solvable systems of two and four equation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000