Quantum Dynamics of a Hydrogen Molecule Confined in a Cylindrical Potential

Loading...
Thumbnail Image
Penn collection
Department of Physics Papers
Degree type
Discipline
Subject
Physics
Quantum Physics
Funder
Grant number
License
Copyright date
Distributor
Related resources
Contributor
Abstract

We study the coupled rotation-vibration levels of a hydrogen molecule in a confining potential with cylindrical symmetry. We include the coupling between rotations and translations and show how this interaction is essential to obtain the correct degeneracies of the energy level scheme. We applied our formalism to study the dynamics of H2 molecules inside a “smooth” carbon nanotube as a function of tube radius. The results are obtained both by numerical solution of the (2J+1)-component radial Schrödinger equation and by developing an effective Hamiltonian to describe the splitting of a manifold of states of fixed angular momentum J and number of phonons N. For nanotube radius smaller than ≈3.5Å, the confining potential has a parabolic shape and the results can be understood in terms of a simple toy model. For larger radius, the potential has the “Mexican hat” shape and therefore the H2 molecule is off centered, yielding radial and tangential translational dynamics in addition to rotational dynamics of H2 molecule which we also describe by a simple model. Finally, we make several predictions for the the neutron scattering observation of various transitions between these levels.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
2003-06-27
Journal title
Physical Review B
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
At the time of publication, author Taner Yildirim was affiliated with the National Institute of Standards and Technology, Gaithersburg, Maryland. Currently, he is a faculty member in the Materials Science and Engineering Department at the University of Pennsylvania.
Recommended citation
Collection