On the improvement of q -deformed hyperbolic functions

In the search of quantum potential models used in the theoretical treatment of diatomic molecules, some of them have been constructed by using standard hyperbolic functions as well as from the so-called q-deformed hyperbolic functions (sc q-dhf). To improve the scope of hyperbolic functions, in this work, a class of generalized q-deformed hyperbolic functions is presented. Specifically, such improvement contains the particular case sc q-dhf besides that the can be expressed in terms of standard hyperbolic functions. As a useful application of the proposal, new q-deformed exactly solvable exponential-type potentials to be used in quantum chemical calculations are given as examples. At this regard, we are considering multi-parameter exponential-type potentials which means that the single choice of each set of q-dependent parameters leads to a different particular case of q-deformed exponential potential totally characterized. That is, with the proposed approach it is not necessary to make use of specialized methods to solve the involved differential equation for each specific case of exponential q-deformed potentials.