Open AccessMatrix Quasi-Exactly Solvable Jacobi Elliptic Hamiltonian
Author(s) -
Ancilla Nininahazwe
Publication year - 2013
Publication title -
open journal of microphysics
Language(s) - English
Resource type - Journals
eISSN - 2162-2469
pISSN - 2162-2450
DOI - 10.4236/ojm.2013.33010
Subject(s) - mathematics , jacobi operator , hamiltonian (control theory) , pure mathematics , jacobi method , algebraic number , jacobi elliptic functions , invariant (physics) , algebra over a field , mathematical physics , mathematical analysis , jacobi polynomials , orthogonal polynomials , mathematical optimization
We construct a new example of 2 × 2-matrix quasi-exactly solvable (QES) Hamiltonian which is associated to a potential depending on the Jacobi elliptic functions. We establish three necessary and sufficient algebraic conditions for the previous operator to have an invariant vector space whose generic elements are polynomials. This operator is called quasi-exactly solvable.