  A mathematical phase-space representation of the 1-dimensional Schr\"odinger
equation is employed to obtain bound and resonance states of the rotationally
excited H$_2$ molecule. The structure of the phase-space tangent field is
analyzed and related to the behavior of the wave function in classically
allowed and forbidden regions. In this phase-space representation, bound states
behave like unstable orbits meanwhile resonance states behave similarly to
asymptotically stable cycles. The lattice of quantum states of the
energy-momentum diagram for H$_2$ is calculated allowing to have a global view
of the energy as function of the quantum numbers. The arc length and winding
number of the phase-space trajectories, as functions of the energy, are used to
obtain the energy eigenvalues of bound and resonance states of H$_2$
