Quantum integrable systems constrained on the sphere
type: Item
instance of: scholarly article
title: Quantum integrable systems constrained on the sphere
zbMATH Open document ID: 0709.58019
DOI: 10.1007/BF00398280
published in: Letters in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: The author proves that the quantized geodesic flow on the sphere \(S^{n- 1}\), the Neumann system (harmonic oscillator constrained on \(S^{n-1})\) and the Rosochatius system are quantum integrable. To prove the integrability the author compares quantization on the cotangent bundle \(T^*S^{n-1}\) with the Weyl transformation induced fron \({\mathbb{R}}^{2n}\), and then calculates the Moyal bracket. The explicit form of the quantum Hamiltonians is given.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 4166106
zbMATH Keywords: quantum integrable system
zbMATH Keywords: geodesic flow
zbMATH Keywords: Neumann system
zbMATH Keywords: Rosochatius system
zbMATH Keywords: quantization
author: Zhangju Liu
reviewed by: Guizhang Tu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4166106