We outline the applications of a new initial condition for the Wheeler-DeWitt equation in various quantum cosmology models. These models consist of minimally coupled scalar field in Friedmann-Robertson-Walker and Stephani spacetimes, varying speed of light theories and conformally coupled scalar field in Friedmann-Robertson-Walker spacetime. This initial condition results in wave packets with complete classical and quantum correspondence. This means that the wave packets closely follow the classical trajectories and strongly peak on them. We show that these models, similar to their classical counterparts, contain singularities even at the quantum level.