Quasi-Exactly Solvable Jacobi Elliptic Potential

Abstract

A new example of 2×2 -matrix quasi-exactly solvable (QES) Hamiltonian which is associated to a Jacobi elliptic potential is constructed. We compute algebraically three necessary and sufficient conditions with the QES analytic method for the Jacobi Hamiltonian to have a finite dimensional invariant vector space. The matrix Jacobi Hamiltonian is called quasi-exactly solvable.