  We introduce a method to construct wave packets with complete classical and
quantum correspondence in one-dimensional non-relativistic quantum mechanics.
First, we consider two similar oscillators with equal total energy. In
classical domain, we can easily solve this model and obtain the trajectories in
the space of variables. This picture in the quantum level is equivalent with a
hyperbolic partial differential equation which gives us a freedom for choosing
the initial wave function and its initial slope. By taking advantage of this
freedom, we propose a method to choose an appropriate initial condition which
is independent from the form of the oscillators. We then construct the wave
packets for some cases and show that these wave packets closely follow the
whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm
interpretation of quantum mechanics to quantify this correspondence and show
that the resulting Bohmian trajectories are also in a complete agreement with
their classical counterparts.
