Ladder Operators for the Rosen-Morse System Through Classical Analogy

In quantum mechanics, ladder operators allow to connect the eigenstates of a system together. Ladder functions are algebraically analog objects defined in the framework of classical hamiltonian physics. For a class of exactly solvable one dimensional Hamiltonians, both the ladder operators and ladder functions take a simple form and there is a close similarity between them. In this work, we show how the analogy extends to the case of the Rosen-Morse Hamiltonian, for which the ladder functions have a more complicated structure. We compute a form for the ladder operators, based on the ladder functions of the system and we analyse the correspondences between both cases. Physical mean values are also obtained as a byproduct of the construction.