منابع مشابه
Quasi exactly solvable matrix Schrödinger operators
Two families of quasi exactly solvable 2 × 2 matrix Schrödinger operators are constructed. The first one is based on a polynomial matrix potential and depends on three parameters. The second is a one-parameter generalisation of the scalar Lamé equation. The relationship between these operators and QES Hamiltonians already considered in the literature is pointed out.
متن کاملQuasi exactly solvable N × N - Matrix Schrödinger operators
New examples of matrix quasi exactly solvable Schrödinger operators are constructed. One of them constitutes a N×N matrix generalization of the quasi exactly solvable anharmonic oscillator, the corresponding invariant vector space is constructed explicitely. Also investigated are matrix generalizations of the Lamé equation.
متن کاملQuasi exactly solvable matrix Schrödinger operators . Yves BRIHAYE Faculté
Two families of quasi exactly solvable 2 × 2 matrix Schrödinger operators are constructed. The first one is based on a polynomial matrix potential and depends on three parameters. The second is a one-parameter generalisation of the scalar Lamé equation. The relationship between these operators and QES Hamiltonians already considered in the literature is pointed out.
متن کاملQuasi exactly solvable operators and Lie superalgebras
Linear operators preserving the direct sum of polynomial rings P(m)⊕P(n) are constructed. In the case |m − n| = 1 they correspond to atypical representations of the superalgebra osp(2,2). For |m − n| = 2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. Examples of Hamiltonians possessing such a hidden algebra are analyzed. PACS numbers: 02.20.Sv, 03.65.Fd ...
متن کاملOn asymptotics of polynomial eigenfunctions for exactly solvable differential operators
In this paper we study the class of differential operators T = Pk j=1 QjD j with polynomial coefficients Qj in one complex variable satisfying the condition degQj ≤ j with equality for at least one j. We show that if degQk < k then the root with the largest modulus of the nth degree eigenpolynomial pn of T tends to infinity when n → ∞, as opposed to the case when degQk = k, which we have treate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Henri Poincaré
سال: 2011
ISSN: 1424-0637,1424-0661
DOI: 10.1007/s00023-011-0077-4