Dynamical algebras of general two-parametric Pöschl–Teller Hamiltonians Original Research Article

A class of operators connecting general two-parametric Pöschl–Teller Hamiltonians is found. These operators include the so-called “shift” (changing only the potential parameters) and “ladder” (changing also the energy eigenvalue) operators. The explicit action on eigenfunctions is computed within a simple and symmetric three-subindex notation. It is shown that the whole set of operators close an image dynamical Lie algebra. A unitary irreducible representation of this image differential realization is characterized.