Phase-space propagation and stability analysis of the 1-dimensional Schrödinger equation for finding bound and resonance states of rotationally excited H 2

Highlights: • Phase-space trajectories of the 1-dimensional radial Schrödinger equation. • Phase-space stability analysis and critical points. • Bound and resonance states obtained from minimizing the arc-length of trajectories. • Bound and resonance states obtained from winding number discontinuities. A phase-space representation of the 1-dimensional Schrödinger equation is employed to obtain bound and resonance states of rotationally excited H${}_2$. 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 like asymptotically stable cycles. 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${}_2$.