Second-Order Supersymmetric Partners of the Trigonometric Rosen–Morse Potential

The second-order supersymmetric partners of the trigonometric Rosen–Morse potential are studied. The stationary Schrodinger equation for this potential is solved in such a way that the general solution supplies straightforwardly the eigenstates of the Hamiltonian while the non-physical solutions turn out to be conveniently expressed for characterizing its global properties. This allows to implement in a simple and systematic way the second-order supersymmetry transformations.