Quantum integrable systems constrained on the sphere (Q921681)

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.