2021/03/15 by Jan Schumm, Schumm, Jan
Physics and Astronomy · #32Q15 #35Q40 #53A20 #53B10 #53B35 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2103.08708
openalex publication_date 2021/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given two c-projectively equivalent metrics on a Kähler manifold we show that the canoncially constructed, Poisson-commuting integrals of motion of the geodesic flow, linear and quadratic in momenta, also commute as quantum operators. The methods employed here also provide a proof of a similar statement in the case of projective equivalence. We also investigate the addition of potentials, i.e. the generalization to natural Hamiltonian systems. We show that the commuting operators lead to separation of variables for Schrödinger's equation.