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A mathematical phase-space representation of the 1-dimensional Schr\"odingerequation is employed to obtain bound and resonance states of the rotationallyexcited H$_2$ molecule. The structure of the phase-space tangent field isanalyzed and related to the behavior of the wave function in classicallyallowed and forbidden regions. In this phase-space representation, bound statesbehave like unstable orbits meanwhile resonance states behave similarly toasymptotically stable cycles. The lattice of quantum states of theenergy-momentum diagram for H$_2$ is calculated allowing to have a global viewof the energy as function of the quantum numbers. The arc length and windingnumber of the phase-space trajectories, as functions of the energy, are used toobtain the energy eigenvalues of bound and resonance states of H$_2$

Phase-space propagation and stability analysis of the 1-dimensional  Schr\"odinger equation for finding bound and resonance states of rotationally  excited H$_2$