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SU (1,1) the hidden dynamical symmetry group for an exact bound state of the Hulthen potential

In this research work, an exact normalised bound eigenstate and energy eigenvalue of the Hulthen potential, for the zero angular momentum within the framework of the non-relativistic time independent Schrödinger wave equation were obtained using the Nikiforov–Uvarov method. Also, their self-adjoint differential creation and annihilation (ladder) operators were derived, andfrom the commutation relations their Casimir operator was defined. These results showed that the non-compact SU(1,1) group is the dynamical group for this exact bound state, described by the representation D+(i) with a spectrum bounded below.