We investigate a class of operators connecting general Hamiltonians of the Poschl-Teller type. The operators involved depend on three parameters and their explicit action on eigenfunctions is found. The whole set of intertwining operators close a su(2,2) ≈ so(4,2) Lie algebra. The space of eigenfunctions supports a differential-difference realization of an irreducible representation of the su(2, 2) algebra.
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