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

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

URL: http://arxiv.org/abs/2006.00095v3
Date: Mon, 30 Aug 2021 13:06:14 GMT
Title: Phase-space propagation and stability analysis of the 1-dimensional Schr\"odinger equation for finding bound and resonance states of rotationally excited H$_2$
Authors: Juan S. Molano, Carlos A. Arango
Abstract summary: 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$$ 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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