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Updated: Jun 23, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
The Heisenberg-Weyl algebra on the circle and a related quantum mechanical model for hindered rotation
Donald J Kouri1, Thomas Markovich, Nicholas Maxwell
1Department of Chemistry, University of Houston, Houston, Texas 77204-5006, USA.
Abstract:
We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.
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