Bound state solutions of the Schrödinger equation and its application to some diatomic molecules.

We apply the supersymmetric quantum mechanics and shape invariance approach to obtain the solutions of the 3-dimensional Schrödinger equation in the presence of a newly proposed potential model called hyperbolic-sinus potential function for any ℓ-state. Rotational-vibrational energy eigenvalues of some diatomic molecules are numerically calculated. Special cases of interest of the hyperbolic-sinus potential function are also studied. Our results indicated that the energy eigenvalue is highly sensitive to the potential parameters.