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arXiv · 2006.00095

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

Juan S. Molano·Carlos A. Arango
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Abstract

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$_2$

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Juan S. Molano, Carlos A. Arango. 2020-05-29. Phase-space propagation and stability analysis of the 1-dimensional Schr\"odinger equation for finding bound and resonance states of rotationally excited H$_2$. https://arxiv.org/abs/2006.00095

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