Quantization in polar coordinates and the phase operator

DOI10.2977/prims/1195165908zbMath0819.46060OpenAlexW2055033290MaRDI QIDQ1343242

Thomas B. Smith, Daniel A. Dubin, Mark A. Hennings

Publication date: 1 February 1995

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195165908

zbMATH Keywords

Poisson bracketquantizationfunctions of radius or anglephase operator for finite quantum systemsposition and momentum variablesWigner-Weyl quantization

Mathematics Subject Classification ID

Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Applications of functional analysis in quantum physics (46N50)

Related Items

Generalized Weyl quantization on the cylinder and the quantum phase, Existence theorems for ordered variants of Weyl quantization, Dequantization techniques for Weyl quantization, How uncertainty bounds the shape index of simple cells, COLLECTIVE AND RELATIVE VARIABLES FOR A CLASSICAL KLEIN–GORDON FIELD, Perturbations of the Landau Hamiltonian: asymptotics of eigenvalue clusters

Uses Software

• Mathematica

Cites Work

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• Phase and number
• Operator symbols in the description of observable-state systems
• Quantum mechanics and partial differential equations
• On the distributions corresponding to bounded operators in the Weyl quantization
• The Moyal product and spectral theory for a class of infinite dimensional matrices
• Remarks on boson commutation rules
• Lie theory and special functions
• Harmonic Analysis in Phase Space. (AM-122)
• On the Quantum Correction For Thermodynamic Equilibrium
• Mathematical Aspects of the Weyl Correspondence
• LAGUERRE POLYNOMIALS, WHITTAKER FUNCTIONS AND THE REPRESENTATIONS OF GROUPS OF BORDERED MATRICES
• Canonically Conjugate Pairs, Uncertainty Relations, and Phase Operators
• Transforms for Operators and Symplectic Automorphisms over a Locally Compact Abelian Group.