A PT-symmetric Hamiltonian associated with a trigonometric Razhavi potential is analyzed. Along the same lines of the general quasi-exactly solvable analytic method considered in the [1][2] [3], three necessary and sufficient algebraic conditions for this Hamiltonian to have a finite-dimensional invariant vector space are established. This PT-symmetric 2 x 2 -matrix Hamiltonian is called quasi-exactlysolvable (QES).
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