Matrix Jacobi Elliptic Hamiltonian and Quasi-Exact Solvability

Ancilla Nininahazwe, Agnès Nakimana, Gloriose Nizigama and Jean Pacifique Munezero

Abstract

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 apply the QES analytic method in order to establish
three necessary and sufficient algebraic conditions for the previous Hamiltonian to have an invariant vector space
whose generic elements are polynomials. This Hamiltonian is called quasi-exactly solvable.