Quantum Mechanics on the cylinder

Abstract

A new approach to deformation quantization on the cylinder considered as phase space is presented. The method is based on the standard Moyal formalism for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The results are compared with other solutions of this problem presented by Kasperkovitz and Peev (Ann. Phys. vol. 230, 21 (1994)0 and by Plebanski and collaborators (Acta Phys. Pol. vol. B 31}, 561 (2000)). The equivalence of these three methods is proved.

21 pages, LaTeX

References in corpus (3)

• Coherent states for a quantum particle on a circle
• Coherent states on the circle
• On the uncertainty relations and squeezed states for the quantum mechanics on a circle

Cited by in corpus (7)

• Quantization of the canonically conjugate pair angle and orbital angular momentum
• Geometrical origin of the *-product in the Fedosov formalism
• From the Weyl quantization of a particle on the circle to number-phase Wigner functions
• Localization properties of squeezed quantum states in nanoscale space domains
• The Boltzmann distribution and the quantum-classical correspondence
• Wigner distribution on a double cylinder phase space for studying quantum error correction protocol
• Coherent states on the circle